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Unit 9: Geometry
About this unit, area and circumference of circles.
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Curriculum / Math / 7th Grade / Unit 4: Equations and Inequalities / Lesson 4
Equations and Inequalities
Lesson 4 of 12
Criteria for Success
Tips for teachers, anchor problems, problem set, target task, additional practice.
Solve equations in the forms $${px+q=r }$$ and $${p(x+q)=r}$$ algebraically.
Common Core Standards
Core standards.
The core standards covered in this lesson
Expressions and Equations
7.EE.B.4.A — Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers. Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?
Foundational Standards
The foundational standards covered in this lesson
6.EE.B.7 — Solve real-world and mathematical problems by writing and solving equations of the form x + p = q and px = q for cases in which p, q and x are all nonnegative rational numbers.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
- Understand that an equation is a statement of balance, and in solving the equation, the balance must be maintained.
- Understand solving an equation as a process of undoing operations using inverse operations that adhere to arithmetic properties.
- Solve equations in the forms $$px+q=r$$ and $$p(x+q)=r$$ .
Suggestions for teachers to help them teach this lesson
In this lesson, students learn the concepts behind the mechanics of solving an equation. In the next two lessons, students will have further opportunities to practice solving equations in contextual situations. Solving equations in these two forms is a fluency expectation in 7th grade. See our Guide to Procedural Skill and Fluency for ideas of activities to use throughout the lesson and remaining part of the unit.
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
A balance is shown below.
a. Describe how you can use the balance to find the value of $$x$$ .
b. Write an equation to represent the situation shown in the balance.
c. Use the equation to model the actions you did in part A with the balance.
d. Repeat parts A–C using the balance shown below.
Guiding Questions
Yoshiro has a new puppy. She decides to create an enclosure for her puppy in her backyard. The enclosure is in the shape of a hexagon, with one pair of opposite sides running the same distance along the length of two parallel flowerbeds. A sketch of the enclosure is shown below.
If the perimeter of the enclosure is 137 feet, what is the length of each side that runs along the flowerbed, labeled $$n$$ in the diagram? Write an equation to represent the situation, and solve using algebraic properties.
Grade 7 Mathematics > Module 2 > Topic C > Lesson 22 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds . © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
Solve the equations:
a. $${12(x-2)=72}$$
b. $${- {1\over3}x+4=-2}$$
c. $${5.6-2p=13}$$
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Solve each equation for the variable. Show every step in your work that maintains the balance in each equation.
a. $${{1\over2}(x+8)=-10}$$
b. $${-5x+12=20}$$
Student Response
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
- Open Up Resources Grade 7 Unit 6 Practice Problems — Lessons 7 and 8, skip review questions
- EngageNY Mathematics Grade 7 Mathematics > Module 2 > Topic C > Lesson 22 — Exercises 1-5, Problem Set
- Kuta Software Free Pre-Algebra Worksheets Two-Step Equations Containing Integers
- Kuta Software Free Algebra 1 Worksheets Two-Step Equations
- Algebra By Example 3.1 Solving 1 and 2 Step Equations
- SolveMe Mobiles — These can be done on the computer, or screen shots can be taken and added to a problem set; stick to one-variable mobiles. Also find good challenges here.
Topic A: Solving and Modeling with Equations
Solve one-step equations with rational numbers.
Represent equations in the forms $${px+q=r}$$ and $${p(x+q)=r}$$ using tape diagrams.
Solve equations in the forms $${px+q=r}$$ and $${p(x+q)=r}$$ using tape diagrams.
7.EE.B.3 7.EE.B.4.A
Solve word problems leading to equations in the forms $${px+q=r}$$ and $${p(x+q)=r}$$ (Part 1).
Solve word problems leading to equations in the forms $${px+q=r}$$ and $${p(x+q)=r }$$ (Part 2).
Model with equations in the form $${px+q=r}$$ and $${p(x+q)=r}$$ .
Create a free account to access thousands of lesson plans.
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Topic B: Solving and Modeling with Inequalities
Solve and graph one-step inequalities.
Write and solve inequalities in the forms $${px+q>r}$$ or $${px+q<r}$$ and $${p(x+q)>r }$$ or $${p(x+q)<r.}$$
Solve inequalities with negative coefficients.
Solve word problems leading to inequalities in the forms $${px+q>r}$$ or $${px+q<r}$$ and $${p(x+q)>r}$$ or $${p(x+q)<r}$$ .
Model with inequalities.
7.EE.B.3 7.EE.B.4.B
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Class 7 Mathematics Worksheets
We have provided below free printable Class 7 Mathematics Worksheets for Download in PDF. The worksheets have been designed based on the latest NCERT Book for Class 7 Mathematics . These Worksheets for Grade 7 Mathematics cover all important topics which can come in your standard 7 tests and examinations. Free printable worksheets for CBSE Class 7 Mathematics , school and class assignments, and practice test papers have been designed by our highly experienced class 7 faculty. You can free download CBSE NCERT printable worksheets for Mathematics Class 7 with solutions and answers. All worksheets and test sheets have been prepared by expert teachers as per the latest Syllabus in Mathematics Class 7. Students can click on the links below and download all Pdf worksheets for Mathematics class 7 for free. All latest Kendriya Vidyalaya Class 7 Mathematics Worksheets with Answers and test papers are given below.
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Here we have the biggest database of free CBSE NCERT KVS Worksheets for Class 7 Mathematics . You can download all free Mathematics worksheets in Pdf for standard 7th. Our teachers have covered Class 7 importantquestions and answers for Mathematics as per the latest curriculum for the current academic year. All test sheets question banks for Class 7 Mathematics and CBSE Worksheets for Mathematics Class 7 will be really useful for Class 7 students to properly prepare for the upcoming tests and examinations. Class 7th students are advised to free download in Pdf all printable workbooks given below.
Topicwise Worksheets for Class 7 Mathematics Download in Pdf
More worksheet for class 7 maths.
Advantages of Solving Class 7 Mathematics Worksheets
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CBSE Worksheets for Class 7 Maths | MCQ Questions for Class 7 Maths
CBSE Worksheets for Class 7 Maths: One of the best teaching strategies employed in most classrooms today is Worksheets. CBSE Class 7 Maths Worksheet for students has been used by teachers & students to develop logical, lingual, analytical, and problem-solving capabilities. So in order to help you with that, we at WorksheetsBuddy have come up with Kendriya Vidyalaya Class 7 Maths Worksheets for the students of Class 7. All our CBSE NCERT Class 7 Maths practice worksheets are designed for helping students to understand various topics, practice skills and improve their subject knowledge which in turn helps students to improve their academic performance. These chapter wise test papers for Class 7 Maths will be useful to test your conceptual understanding.
Board: Central Board of Secondary Education(www.cbse.nic.in) Subject: Class 7 Maths Number of Worksheets: 85
CBSE Class 7 Maths Worksheets PDF
All the CBSE Worksheets for Class 7 Maths provided in this page are provided for free which can be downloaded by students, teachers as well as by parents. We have covered all the Class 7 Maths important questions and answers in the worksheets which are included in CBSE NCERT Syllabus. Just click on the following link and download the CBSE Class 7 Maths Worksheet. CBSE Worksheets for Class 7 Math can also use like assignments for Class 7 Maths students.
- MCQ Questions for Class 7 Maths
- Grade 7 Integers Worksheets
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- Grade 7 Simple Equations Worksheets
- Grade 7 Lines and Angles Worksheets
- Grade 7 The Triangles and its Properties Worksheets
- Grade 7 Congruence of Triangles Worksheets
- Grade 7 Comparing Quantities Worksheets
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- Grade 7 Practical Geometry Worksheets
- Grade 7 Perimeter And Area Worksheets
- Grade 7 Algebraic Expressions Worksheets
- Grade 7 Exponents and Powers Worksheets
- Grade 7 Symmetry Worksheets
- Grade 7 Visualising Solid Shapes Worksheets
CBSE Worksheets for Class 7 Maths Algebraic
- CBSE Worksheets for Class 7 Maths Algebraic Expression Assignment 1
- CBSE Worksheets for Class 7 Maths Algebraic Expression Assignment 2
- CBSE Worksheets for Class 7 Maths Algebraic Expression Assignment 3
- CBSE Worksheets for Class 7 Maths Algebraic Expression Assignment 4
CBSE Worksheets for Class 7 Maths Comparing Quantities
- CBSE Worksheets for Class 7 Maths Comparing Quantities Assignment
CBSE Worksheets for Class 7 Maths Congruence of Triangles
- CBSE Worksheets for Class 7 Maths Congruence of Triangles Assignment 1
- CBSE Worksheets for Class 7 Maths Congruence of Triangles Assignment 2
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- CBSE Worksheets for Class 7 Maths Congruence of Triangles Assignment 4
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CBSE Worksheets for Class 7 Maths Data Handling
- CBSE Worksheets for Class 7 Maths Data Handling Assignment 1
- CBSE Worksheets for Class 7 Maths Data Handling Assignment 2
- CBSE Worksheets for Class 7 Maths Data Handling Assignment 3
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CBSE Worksheets for Class 7 Maths Exponents & Powers
- CBSE Worksheets for Class 7 Maths Exponents & Powers Assignment 1
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CBSE Worksheets for Class 7 Maths Fractions and Decimals
- CBSE Worksheets for Class 7 Maths Fractions and Decimals Assignment 1
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- CBSE Worksheets for Class 7 Maths Fractions and Decimals Assignment 7
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- CBSE Worksheets for Class 7 Maths Fractions and Decimals Assignment 9
CBSE Worksheets for Class 7 Maths Integers
- CBSE Worksheets for Class 7 Maths Integers Assignment 1
- CBSE Worksheets for Class 7 Maths Integers Assignment 2
- CBSE Worksheets for Class 7 Maths Integers Assignment 3
- CBSE Worksheets for Class 7 Maths Integers Assignment 4
- CBSE Worksheets for Class 7 Maths Integers Assignment 5
- CBSE Worksheets for Class 7 Maths Integers Assignment 6
- CBSE Worksheets for Class 7 Maths Integers Assignment 7
CBSE Worksheets for Class 7 Maths Lines and Angles
- CBSE Worksheets for Class 7 Maths Lines and Angles Assignment 1
- CBSE Worksheets for Class 7 Maths Lines and Angles Assignment 2
- CBSE Worksheets for Class 7 Maths Lines and Angles Assignment 3
- CBSE Worksheets for Class 7 Maths Lines and Angles Assignment 4
- CBSE Worksheets for Class 7 Maths Lines and Angles Assignment 5
- CBSE Worksheets for Class 7 Maths Lines and Angles Assignment 6
CBSE Worksheets for Class 7 Maths Perimeter and Area
- CBSE Worksheets for Class 7 Maths Perimeter and Area Assignment 1
- CBSE Worksheets for Class 7 Maths Perimeter and Area Assignment 2
CBSE Worksheets for Class 7 Maths Rational Numbers
- CBSE Worksheets for Class 7 Maths Rational Numbers Assignment 1
- CBSE Worksheets for Class 7 Maths Rational Numbers Assignment 2
- CBSE Worksheets for Class 7 Maths Rational Numbers Assignment 3
- CBSE Worksheets for Class 7 Maths Rational Numbers Assignment 4
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- CBSE Worksheets for Class 7 Maths Rational Numbers Assignment 6
CBSE Worksheets for Class 7 Maths Simple Equations
- CBSE Worksheets for Class 7 Maths Simple Equations Assignment 1
- CBSE Worksheets for Class 7 Maths Simple Equations Assignment 2
- CBSE Worksheets for Class 7 Maths Simple Equations Assignment 3
- CBSE Worksheets for Class 7 Maths Simple Equations Assignment 4
CBSE Worksheets for Class 7 Maths symmetry
- CBSE Worksheets for Class 7 Maths symmetry Assignment
CBSE Worksheets for Class 7 Maths Triangle and its Properties
- CBSE Worksheets for Class 7 Maths Triangle and its Properties Assignment 1
- CBSE Worksheets for Class 7 Maths Triangle and its Properties Assignment 2
- CBSE Worksheets for Class 7 Maths Triangle and its Properties Assignment 3
- CBSE Worksheets for Class 7 Maths Triangle and its Properties Assignment 4
- CBSE Worksheets for Class 7 Maths Triangle and its Properties Assignment 5
- CBSE Worksheets for Class 7 Maths Comparing Quantities Assignment 1
- CBSE Worksheets for Class 7 Maths Comparing Quantities Assignment 2
- CBSE Worksheets for Class 7 Maths Comparing Quantities Assignment 3
Class 7 Maths Worksheets
- CBSE Worksheets for Class 7 Mathematics Assignment 1
- CBSE Worksheets for Class 7 Mathematics Assignment 2
- CBSE Worksheets for Class 7 Mathematics Assignment 3
- CBSE Worksheets for Class 7 Mathematics Assignment 4
- CBSE Worksheets for Class 7 Mathematics Assignment 5
- CBSE Worksheets for Class 7 Mathematics Assignment 6
- CBSE Worksheets for Class 7 Mathematics Assignment 7
- CBSE Worksheets for Class 7 Mathematics Assignment 8
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- CBSE Worksheets for Class 7 Mathematics Assignment 12
- CBSE Worksheets for Class 7 Mathematics Assignment 13
- CBSE Worksheets for Class 7 Mathematics Assignment 14
- CBSE Worksheets for Class 7 Mathematics Assignment 15
- CBSE Worksheets for Class 7 Mathematics Assignment 16
Advantages of CBSE Class 7 Maths Worksheets
- By practising NCERT CBSE Class 7 Maths Worksheet , students can improve their problem solving skills.
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Worksheets of CBSE Class 7 Maths are devised by experts of WorksheetsBuddy experts who have great experience and expertise in teaching Maths. So practising these worksheets will promote students problem-solving skills and subject knowledge in an interactive method. Students can also download CBSE Class 7 Maths Chapter wise question bank pdf and access it anytime, anywhere for free. Browse further to download free CBSE Class 7 Maths Worksheets PDF .
Now that you are provided all the necessary information regarding CBSE Class 7 Maths Worksheet and we hope this detailed article is helpful. So Students who are preparing for the exams must need to have great solving skills. And in order to have these skills, one must practice enough of Class 7 Math revision worksheets . And more importantly, students should need to follow through the worksheets after completing their syllabus. Working on CBSE Class 7 Maths Worksheets will be a great help to secure good marks in the examination. So start working on Class 7 Math Worksheets to secure good score.
CBSE Worksheets For Class 7
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Common Core State Standards Initiative
Grade 7 » The Number System
Standards in this domain:, apply and extend previous understandings of operations with fractions..
1 Computations with rational numbers extend the rules for manipulating fractions to complex fractions.
- Standards for Mathematical Practice
- How to read the grade level standards
- Introduction
- Counting & Cardinality
- Operations & Algebraic Thinking
- Number & Operations in Base Ten
- Measurement & Data
- Number & Operations—Fractions¹
- Number & Operations in Base Ten¹
- Number & Operations—Fractions
- Ratios & Proportional Relationships
- The Number System
- Expressions & Equations
- Statistics & Probability
- The Real Number System
- Quantities*
- The Complex Number System
- Vector & Matrix Quantities
- Seeing Structure in Expressions
- Arithmetic with Polynomials & Rational Expressions
- Creating Equations*
- Reasoning with Equations & Inequalities
- Interpreting Functions
- Building Functions
- Linear, Quadratic, & Exponential Models*
- Trigonometric Functions
- High School: Modeling
- Similarity, Right Triangles, & Trigonometry
- Expressing Geometric Properties with Equations
- Geometric Measurement & Dimension
- Modeling with Geometry
- Interpreting Categorical & Quantitative Data
- Making Inferences & Justifying Conclusions
- Conditional Probability & the Rules of Probability
- Using Probability to Make Decisions
- Courses & Transitions
- Mathematics Glossary
- Mathematics Appendix A
- NCERT Solutions
- NCERT Class 7
- NCERT 7 Maths
- Chapter 5 Lines And Angles
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles
NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles are the best study materials for those students who are finding difficulties in solving problems. These NCERT Solutions can help students clear doubts quickly and help in understanding the topic effectively. Students who wish to score good marks in Maths should practise NCERT Solutions for Class 7 Maths.
Download Exclusively Curated Chapter Notes for Class 7 Maths Chapter – 5 Lines and Angles
Download most important questions for class 7 maths chapter – 5 lines and angles.
Chapter 5 – Lines and Angles of NCERT Solutions for Class 7 Maths contain 2 exercises. Let us now have a quick glance at some of the topics covered in this chapter.
- Introduction to Lines and Angles
- Complementary Angles
- Supplementary Angles
- Adjacent Angles
- Linear Pair
- Vertically Opposite Angles
- Intersecting Lines
- Transversal
- Angles made by a Transversal
- Transversal of Parallel Lines
- Checking for Parallel Lines
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Access Exercises of NCERT Solutions for Class 7 Maths Chapter 5 Lines and Angles
Exercise 5.1 Solutions
Exercise 5.2 Solutions
Access answers to NCERT Solutions for Class 7 Maths Chapter 5 – Lines and Angles
Exercise 5.1 Page: 101
1. Find the complement of each of the following angles:
Two angles are said to be complementary if the sum of their measures is 90 o .
The given angle is 20 o
Let the measure of its complement be x o .
= x + 20 o = 90 o
= x = 90 o – 20 o
Hence, the complement of the given angle measures 70 o .
The given angle is 63 o
= x + 63 o = 90 o
= x = 90 o – 63 o
Hence, the complement of the given angle measures 27 o .
The given angle is 57 o
= x + 57 o = 90 o
= x = 90 o – 57 o
Hence, the complement of the given angle measures 33 o .
2. Find the supplement of each of the following angles:
Two angles are said to be supplementary if the sum of their measures is 180 o .
The given angle is 105 o
Let the measure of its supplement be x o .
= x + 105 o = 180 o
= x = 180 o – 105 o
Hence, the supplement of the given angle measures 75 o .
The given angle is 87 o
= x + 87 o = 180 o
= x = 180 o – 87 o
Hence, the supplement of the given angle measures 93 o .
The given angle is 154 o
= x + 154 o = 180 o
= x = 180 o – 154 o
3. Identify which of the following pairs of angles are complementary and which are supplementary.
(i) 65 o , 115 o
We have to find the sum of given angles to identify whether the angles are complementary or supplementary.
= 65 o + 115 o
If the sum of two angle measures is 180 o , then the two angles are said to be supplementary.
∴ These angles are supplementary angles.
(ii) 63 o , 27 o
= 63 o + 27 o
If the sum of two angle measures is 90 o , then the two angles are said to be complementary.
∴ These angles are complementary angles.
(iii) 112 o , 68 o
= 112 o + 68 o
(iv) 130 o , 50 o
= 130 o + 50 o
(v) 45 o , 45 o
= 45 o + 45 o
(vi) 80 o , 10 o
= 80 o + 10 o
4. Find the angles which are equal to their complement.
Let the measure of the required angle be x o .
We know that the sum of measures of complementary angle pair is 90 o .
= x + x = 90 o
= 2x = 90 o
Hence, the required angle measure is 45 o .
5. Find the angles which are equal to their supplement.
We know that the sum of measures of supplementary angle pair is 180 o .
= x + x = 180 o
= 2x = 180 o
= x = 180/2
Hence, the required angle measure is 90 o .
6. In the given figure, ∠1 and ∠2 are supplementary angles. If ∠1 is decreased, what changes should take place in ∠2 so that both angles still remain supplementary?
From the question, it is given that
∠1 and ∠2 are supplementary angles.
If ∠1 is decreased, then ∠2 must be increased by the same value. Hence, this angle pair remains supplementary.
7. Can two angles be supplementary if both of them are:
(i). Acute?
No. If two angles are acute, which means less than 90 o , then they cannot be supplementary because their sum will always be less than 90 o .
(ii). Obtuse?
No. If two angles are obtuse, which means more than 90 o , then they cannot be supplementary because their sum will always be more than 180 o .
(iii). Right?
Yes. If two angles are right, which means both measure 90 o , then they can form a supplementary pair.
∴ 90 o + 90 o = 180
8. An angle is greater than 45 o . Is its complementary angle greater than 45 o or equal to 45 o or less than 45 o ?
Let us assume the complementary angles be p and q,
= p + q = 90 o
It is given in the question that p > 45 o
Adding q on both sides,
= p + q > 45 o + q
= 90 o > 45 o + q
= 90 o – 45 o > q
= q < 45 o
Hence, its complementary angle is less than 45 o .
9. In the adjoining figure:
(i) Is ∠1 adjacent to ∠2?
By observing the figure, we came to conclude that,
Yes, as ∠1 and ∠2 have a common vertex, i.e., O and a common arm, OC.
Their non-common arms, OA and OE, are on both sides of the common arm.
(ii) Is ∠AOC adjacent to ∠AOE?
No, since they have a common vertex O and common arm OA.
But, they have no non-common arms on both sides of the common arm.
(iii) Do ∠COE and ∠EOD form a linear pair?
Yes, as ∠COE and ∠EOD have a common vertex, i.e. O and a common arm OE.
Their non-common arms, OC and OD, are on both sides of the common arm.
(iv) Are ∠BOD and ∠DOA supplementary?
Yes, as ∠BOD and ∠DOA have a common vertex, i.e. O and a common arm OE.
Their non-common arms, OA and OB, are opposite to each other.
(v) Is ∠1 vertically opposite to ∠4?
Yes, ∠1 and ∠2 are formed by the intersection of two straight lines AB and CD.
(vi) What is the vertically opposite angle of ∠5?
∠COB is the vertically opposite angle of ∠5. Because these two angles are formed by the intersection of two straight lines AB and CD.
10. Indicate which pairs of angles are:
(i) Vertically opposite angles.
By observing the figure, we can say that
∠1 and ∠4, ∠5 and ∠2 + ∠3 are vertically opposite angles. Because these two angles are formed by the intersection of two straight lines.
(ii) Linear pairs.
By observing the figure, we can say that,
∠1 and ∠5, ∠5 and ∠4, as these have a common vertex and also have non-common arms opposite to each other.
11. In the following figure, is ∠1 adjacent to ∠2? Give reasons.
∠1 and ∠2 are not adjacent angles because they are not lying on the same vertex.
12. Find the values of the angles x, y, and z in each of the following:
∠x = 55 o , because vertically opposite angles.
∠x + ∠y = 180 o … [∵ linear pair]
= 55 o + ∠y = 180 o
= ∠y = 180 o – 55 o
= ∠y = 125 o
Then, ∠y = ∠z … [∵ vertically opposite angles]
∴ ∠z = 125 o
∠z = 40 o , because vertically opposite angles.
∠y + ∠z = 180 o … [∵ linear pair]
= ∠y + 40 o = 180 o
= ∠y = 180 o – 40 o
= ∠y = 140 o
Then, 40 + ∠x + 25 = 180 o … [∵angles on straight line]
65 + ∠x = 180 o
∠x = 180 o – 65
∴ ∠x = 115 o
13. Fill in the blanks.
(i) If two angles are complementary, then the sum of their measures is _______.
If two angles are complementary, then the sum of their measures is 90 o .
(ii) If two angles are supplementary, then the sum of their measures is ______.
If two angles are supplementary, then the sum of their measures is 180 o .
(iii) Two angles forming a linear pair are _______________.
Two angles forming a linear pair are supplementary.
(iv) If two adjacent angles are supplementary, they form a ___________.
If two adjacent angles are supplementary, they form a linear pair.
(v) If two lines intersect at a point, then the vertically opposite angles are always
_____________.
If two lines intersect at a point, then the vertically opposite angles are always equal.
(vi) If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are __________.
If two lines intersect at a point, and if one pair of vertically opposite angles are acute angles, then the other pair of vertically opposite angles are obtuse angles.
14. In the adjoining figure, name the following pairs of angles.
(i) Obtuse vertically opposite angles
∠AOD and ∠BOC are obtuse vertically opposite angles in the given figure.
(ii) Adjacent complementary angles
∠EOA and ∠AOB are adjacent complementary angles in the given figure.
(iii) Equal supplementary angles
∠EOB and EOD are the equal supplementary angles in the given figure.
(iv) Unequal supplementary angles
∠EOA and ∠EOC are the unequal supplementary angles in the given figure.
(v) Adjacent angles that do not form a linear pair
∠AOB and ∠AOE, ∠AOE and ∠EOD, ∠EOD and ∠COD are the adjacent angles that do not form a linear pair in the given figure.
Exercise 5.2 Page: 110
1. State the property that is used in each of the following statements?
(i) If a ∥ b, then ∠1 = ∠5.
Corresponding angles property is used in the above statement.
(ii) If ∠4 = ∠6, then a ∥ b.
Alternate interior angles property is used in the above statement.
(iii) If ∠4 + ∠5 = 180 o , then a ∥ b.
Interior angles on the same side of the transversal are supplementary.
2. In the adjoining figure, identify
(i) The pairs of corresponding angles.
By observing the figure, the pairs of the corresponding angles are,
∠1 and ∠5, ∠4 and ∠8, ∠2 and ∠6, ∠3 and ∠7
(ii) The pairs of alternate interior angles.
By observing the figure, the pairs of alternate interior angles are,
∠2 and ∠8, ∠3 and ∠5
(iii) The pairs of interior angles on the same side of the transversal.
By observing the figure, the pairs of interior angles on the same side of the transversal are ∠2 and ∠5, ∠3 and ∠8
(iv) The vertically opposite angles.
By observing the figure, the vertically opposite angles are,
∠1 and ∠3, ∠5 and ∠7, ∠2 and ∠4, ∠6 and ∠8
3. In the adjoining figure, p ∥ q. Find the unknown angles.
By observing the figure,
∠d = ∠125 o … [∵ corresponding angles]
We know that Linear pair is the sum of adjacent angles is 180 o
= ∠e + 125 o = 180 o … [Linear pair]
= ∠e = 180 o – 125 o
= ∠e = 55 o
From the rule of vertically opposite angles,
∠f = ∠e = 55 o
∠b = ∠d = 125 o
By the property of corresponding angles,
∠c = ∠f = 55 o
∠a = ∠e = 55 o
4. Find the value of x in each of the following figures if l ∥ m.
Let us assume the other angle on the line m be ∠y.
= ∠x + ∠y = 180 o
= ∠x + 110 o = 180 o
= ∠x = 180 o – 110 o
= ∠x = 70 o
5. In the given figure, the arms of the two angles are parallel.
If ∠ABC = 70 o , then find
(i) Let us consider AB ∥ DG.
BC is the transversal line intersecting AB and DG.
By the property of corresponding angles
∠DGC = ∠ABC
∠DGC = 70 o
(ii) Let us consider that BC ∥ EF.
DE is the transversal line intersecting BC and EF.
∠DEF = ∠DGC
∠DEF = 70 o
6. In the given figures below, decide whether l is parallel to m.
Let us consider the two lines, l and m.
n is the transversal line intersecting l and m.
We know that the sum of interior angles on the same side of the transversal is 180 o .
= 126 o + 44 o
But, the sum of interior angles on the same side of transversal is not equal to 180 o .
So, line l is not parallel to line m.
Let us assume ∠x be the vertically opposite angle formed due to the intersection of the straight line l and transversal n,
Then, ∠x = 75 o
= 75 o + 75 o
Let us assume ∠x be the vertically opposite angle formed due to the intersection of the straight line l and transversal line n.
= 123 o + ∠x
= 123 o + 57 o
∴ The sum of interior angles on the same side of the transversal is equal to 180 o .
So, line l is parallel to line m.
Let us assume ∠x be the angle formed due to the intersection of the Straight line l and transversal line n.
We know that the Linear pair is the sum of adjacent angles equal to 180 o .
= ∠x + 98 o = 180 o
= ∠x = 180 o – 98 o
= ∠x = 82 o
Now, we consider ∠x and 72 o are the corresponding angles.
For l and m to be parallel to each other, corresponding angles should be equal.
But, in the given figure, corresponding angles measure 82 o and 72 o , respectively.
∴ Line l is not parallel to line m.
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