Class 9 Exam > Class 9 Notes > Mathematics (Maths) Class 9 > RS Aggarwal Solutions: Lines and Angles- 1
RS Aggarwal Solutions: Lines and Angles- 1 | Mathematics (Maths) Class 9 PDF Download
| Download, print and study this document offline |
Please wait while the PDF view is loading
Page 1
Question:1
Define the following terms:
i
Angle
ii
Interior of an angle
iii
Obtuse angle
iv
Reflex angle
v
Complementary angles
vi
Supplementary angles
Solution:
i
Two rays OA and OB, with a common end-point O, form an angle AOB that is represented as ?AOB
.
ii
The interior of an angle is the set of all points in its plane, which lie on the same side of OA as B and also on the same side of OB as A.
iii
An angle greater than 90°
but less than 180°
is called an obtuse angle.
iv
An angle greater than 180°
but less than 360°
is called a reflex angle.
v
Two angles are said to be complementary if the sum of their measures is 90°
.
vi
Two angles are said to be supplementary if the sum of their measures is 180°
.
Question:2
Find the complement of each of the following angles.
i
55°
ii
16°
iii
iv
2
3
of a right angle
Solution:
Two angles whose sum is 90° are called complementary angles.
i
Complement of 55° = 90° - 55° = 35°
ii
Complement of 16° = (90 -16)°
= 74°
90°
Page 2
Question:1
Define the following terms:
i
Angle
ii
Interior of an angle
iii
Obtuse angle
iv
Reflex angle
v
Complementary angles
vi
Supplementary angles
Solution:
i
Two rays OA and OB, with a common end-point O, form an angle AOB that is represented as ?AOB
.
ii
The interior of an angle is the set of all points in its plane, which lie on the same side of OA as B and also on the same side of OB as A.
iii
An angle greater than 90°
but less than 180°
is called an obtuse angle.
iv
An angle greater than 180°
but less than 360°
is called a reflex angle.
v
Two angles are said to be complementary if the sum of their measures is 90°
.
vi
Two angles are said to be supplementary if the sum of their measures is 180°
.
Question:2
Find the complement of each of the following angles.
i
55°
ii
16°
iii
iv
2
3
of a right angle
Solution:
Two angles whose sum is 90° are called complementary angles.
i
Complement of 55° = 90° - 55° = 35°
ii
Complement of 16° = (90 -16)°
= 74°
90°
iii
Complement of 90° = 90° - 90° = 0°
iv
2
3
of a right angle ? 90 ×
2
3
° = 60°
Complement of
2
3
of a right angle = (90 -60)° = 30°
Question:3
Find the supplement of each of the following angles.
i
42°
ii
90°
iii
124°
iv
3
5
of a right angle
Solution:
Two angles whose sum is 180° are called supplementary angles.
i
Supplement of 42° = 180° - 42° = 138°
ii
Supplement of 90° = 180° - 90° = 90°
iii
Supplement of 124° = 180° - 124° = 56°
iv
3
5
of a right angle ?
3
5
×90 = 54°
Supplement of
3
5
of a right angle = (180 -54)° = 126°
Question:4
Find the measure of an angle which is
i
equal to its complement
ii
equal to its supplement
Solution:
i
Let the measure of the required angle be x°
.
Then, in case of complementary angles:
x +x = 90° ? 2x = 90° ? x = 45°
Hence, measure of the angle that is equal to its complement is 45°
.
ii
Let the measure of the required angle be x°
?.
Then, in case of supplementary angles:
x +x = 180° ? 2x = 180° ? x = 90°
Hence, measure of the angle that is equal to its supplement is 90°
.
Question:5
Find the measure of an angle which is 36° more than its complement.
Solution:
Let the measure of the required angle be x°
.
Then, measure of its complement = (90 -x)°
.
Therefore,
x -(90°-x) = 36° ? 2x = 126° ? x = 63°
Hence, the measure of the required angle is 63°
.
Question:6
Find the measure of an angle which is 30° less than its supplement.
Solution:
Let the measure of the angle be x°.
? Supplement of x° = 180° - x°
It is given that,
( )
( )
Page 3
Question:1
Define the following terms:
i
Angle
ii
Interior of an angle
iii
Obtuse angle
iv
Reflex angle
v
Complementary angles
vi
Supplementary angles
Solution:
i
Two rays OA and OB, with a common end-point O, form an angle AOB that is represented as ?AOB
.
ii
The interior of an angle is the set of all points in its plane, which lie on the same side of OA as B and also on the same side of OB as A.
iii
An angle greater than 90°
but less than 180°
is called an obtuse angle.
iv
An angle greater than 180°
but less than 360°
is called a reflex angle.
v
Two angles are said to be complementary if the sum of their measures is 90°
.
vi
Two angles are said to be supplementary if the sum of their measures is 180°
.
Question:2
Find the complement of each of the following angles.
i
55°
ii
16°
iii
iv
2
3
of a right angle
Solution:
Two angles whose sum is 90° are called complementary angles.
i
Complement of 55° = 90° - 55° = 35°
ii
Complement of 16° = (90 -16)°
= 74°
90°
iii
Complement of 90° = 90° - 90° = 0°
iv
2
3
of a right angle ? 90 ×
2
3
° = 60°
Complement of
2
3
of a right angle = (90 -60)° = 30°
Question:3
Find the supplement of each of the following angles.
i
42°
ii
90°
iii
124°
iv
3
5
of a right angle
Solution:
Two angles whose sum is 180° are called supplementary angles.
i
Supplement of 42° = 180° - 42° = 138°
ii
Supplement of 90° = 180° - 90° = 90°
iii
Supplement of 124° = 180° - 124° = 56°
iv
3
5
of a right angle ?
3
5
×90 = 54°
Supplement of
3
5
of a right angle = (180 -54)° = 126°
Question:4
Find the measure of an angle which is
i
equal to its complement
ii
equal to its supplement
Solution:
i
Let the measure of the required angle be x°
.
Then, in case of complementary angles:
x +x = 90° ? 2x = 90° ? x = 45°
Hence, measure of the angle that is equal to its complement is 45°
.
ii
Let the measure of the required angle be x°
?.
Then, in case of supplementary angles:
x +x = 180° ? 2x = 180° ? x = 90°
Hence, measure of the angle that is equal to its supplement is 90°
.
Question:5
Find the measure of an angle which is 36° more than its complement.
Solution:
Let the measure of the required angle be x°
.
Then, measure of its complement = (90 -x)°
.
Therefore,
x -(90°-x) = 36° ? 2x = 126° ? x = 63°
Hence, the measure of the required angle is 63°
.
Question:6
Find the measure of an angle which is 30° less than its supplement.
Solution:
Let the measure of the angle be x°.
? Supplement of x° = 180° - x°
It is given that,
( )
( )
(180° - x°) - x° = 30°
? 180° - 2x°= 30°
? 2x° = 180° - 30° = 150°
? x° = 75°
Thus, the measure of the angle is 75°.
Question:7
Find the angle which is four times its complement.
Solution:
Let the measure of the required angle be x
.
Then, measure of its complement = (90°-x)
.
Therefore,
x = (90°-x)4 ? x = 360°-4x ? 5x = 360° ? x = 72°
Hence, the measure of the required angle is 72°
.
Question:8
Find the angle which is five times its supplement.
Solution:
Let the measure of the required angle be x
.
Then, measure of its supplement = (180°-x)
.
Therefore,
x = (180°-x)5 ? x = 900°-5x ? 6x = 900° ? x = 150°
Hence, the measure of the required angle is 150°
.
Question:9
Find the angle whose supplement is four times its complement.
Solution:
Let the measure of the required angle be x°
.
Then, measure of its complement = (90 -x)°
.
And, measure of its supplement = (180 -x)°
.
Therefore,
(180 -x) = 4(90 -x) ? 180 -x = 360 -4x ? 3x = 180 ? x = 60
Hence, the measure of the required angle is 60°
.
Question:10
Find the angle whose complement is one-third of its supplement.
Solution:
Let the measure of the required angle be x°
.
Then, the measure of its complement = (90 -x)°
.
And the measure of its supplement = (180 -x)°
.
Therefore,
(90 -x) =
1
3
(180 -x) ? 3(90 -x) = (180 -x) ? 270 -3x = 180 -x ? 2x = 90 ? x = 45
Hence, the measure of the required angle is 45°
.
Question:11
Two complementary angles are in the ratio 4 : 5. Find the angles.
Solution:
Let the two angles be 4x and 5x, respectively.
Then,
4x +5x = 90 ? 9x = 90 ? x = 10°
Hence, the two angles are 4x = 4 ×10° = 40° and 5x = 5 ×10° = 50°
.
Question:12
Find the value of x for which the angles (2x – 5)° and (x – 10)° are the complementary angles.
Solution:
Two angles whose sum is 90° are called complementary angles.
It is given that the angles (2x – 5)° and (x – 10)° are the complementary angles.
? (2x – 5)° + (x – 10)° = 90°
? 3x° – 15° = 90°
Page 4
Question:1
Define the following terms:
i
Angle
ii
Interior of an angle
iii
Obtuse angle
iv
Reflex angle
v
Complementary angles
vi
Supplementary angles
Solution:
i
Two rays OA and OB, with a common end-point O, form an angle AOB that is represented as ?AOB
.
ii
The interior of an angle is the set of all points in its plane, which lie on the same side of OA as B and also on the same side of OB as A.
iii
An angle greater than 90°
but less than 180°
is called an obtuse angle.
iv
An angle greater than 180°
but less than 360°
is called a reflex angle.
v
Two angles are said to be complementary if the sum of their measures is 90°
.
vi
Two angles are said to be supplementary if the sum of their measures is 180°
.
Question:2
Find the complement of each of the following angles.
i
55°
ii
16°
iii
iv
2
3
of a right angle
Solution:
Two angles whose sum is 90° are called complementary angles.
i
Complement of 55° = 90° - 55° = 35°
ii
Complement of 16° = (90 -16)°
= 74°
90°
iii
Complement of 90° = 90° - 90° = 0°
iv
2
3
of a right angle ? 90 ×
2
3
° = 60°
Complement of
2
3
of a right angle = (90 -60)° = 30°
Question:3
Find the supplement of each of the following angles.
i
42°
ii
90°
iii
124°
iv
3
5
of a right angle
Solution:
Two angles whose sum is 180° are called supplementary angles.
i
Supplement of 42° = 180° - 42° = 138°
ii
Supplement of 90° = 180° - 90° = 90°
iii
Supplement of 124° = 180° - 124° = 56°
iv
3
5
of a right angle ?
3
5
×90 = 54°
Supplement of
3
5
of a right angle = (180 -54)° = 126°
Question:4
Find the measure of an angle which is
i
equal to its complement
ii
equal to its supplement
Solution:
i
Let the measure of the required angle be x°
.
Then, in case of complementary angles:
x +x = 90° ? 2x = 90° ? x = 45°
Hence, measure of the angle that is equal to its complement is 45°
.
ii
Let the measure of the required angle be x°
?.
Then, in case of supplementary angles:
x +x = 180° ? 2x = 180° ? x = 90°
Hence, measure of the angle that is equal to its supplement is 90°
.
Question:5
Find the measure of an angle which is 36° more than its complement.
Solution:
Let the measure of the required angle be x°
.
Then, measure of its complement = (90 -x)°
.
Therefore,
x -(90°-x) = 36° ? 2x = 126° ? x = 63°
Hence, the measure of the required angle is 63°
.
Question:6
Find the measure of an angle which is 30° less than its supplement.
Solution:
Let the measure of the angle be x°.
? Supplement of x° = 180° - x°
It is given that,
( )
( )
(180° - x°) - x° = 30°
? 180° - 2x°= 30°
? 2x° = 180° - 30° = 150°
? x° = 75°
Thus, the measure of the angle is 75°.
Question:7
Find the angle which is four times its complement.
Solution:
Let the measure of the required angle be x
.
Then, measure of its complement = (90°-x)
.
Therefore,
x = (90°-x)4 ? x = 360°-4x ? 5x = 360° ? x = 72°
Hence, the measure of the required angle is 72°
.
Question:8
Find the angle which is five times its supplement.
Solution:
Let the measure of the required angle be x
.
Then, measure of its supplement = (180°-x)
.
Therefore,
x = (180°-x)5 ? x = 900°-5x ? 6x = 900° ? x = 150°
Hence, the measure of the required angle is 150°
.
Question:9
Find the angle whose supplement is four times its complement.
Solution:
Let the measure of the required angle be x°
.
Then, measure of its complement = (90 -x)°
.
And, measure of its supplement = (180 -x)°
.
Therefore,
(180 -x) = 4(90 -x) ? 180 -x = 360 -4x ? 3x = 180 ? x = 60
Hence, the measure of the required angle is 60°
.
Question:10
Find the angle whose complement is one-third of its supplement.
Solution:
Let the measure of the required angle be x°
.
Then, the measure of its complement = (90 -x)°
.
And the measure of its supplement = (180 -x)°
.
Therefore,
(90 -x) =
1
3
(180 -x) ? 3(90 -x) = (180 -x) ? 270 -3x = 180 -x ? 2x = 90 ? x = 45
Hence, the measure of the required angle is 45°
.
Question:11
Two complementary angles are in the ratio 4 : 5. Find the angles.
Solution:
Let the two angles be 4x and 5x, respectively.
Then,
4x +5x = 90 ? 9x = 90 ? x = 10°
Hence, the two angles are 4x = 4 ×10° = 40° and 5x = 5 ×10° = 50°
.
Question:12
Find the value of x for which the angles (2x – 5)° and (x – 10)° are the complementary angles.
Solution:
Two angles whose sum is 90° are called complementary angles.
It is given that the angles (2x – 5)° and (x – 10)° are the complementary angles.
? (2x – 5)° + (x – 10)° = 90°
? 3x° – 15° = 90°
? 3x° = 90° + 15° = 105°
? x° =
105°
3
= 35°
Thus, the value of x is 35.
Read More
|
44 videos|412 docs|55 tests
|
FAQs on RS Aggarwal Solutions: Lines and Angles- 1 - Mathematics (Maths) Class 9
| 1. What are lines and angles? |  |
Ans. Lines and angles are fundamental concepts in geometry. A line is a straight path that extends indefinitely in both directions. An angle is formed when two rays share a common endpoint called the vertex. It is measured in degrees and can be acute, right, obtuse, or straight.
| 2. How do you classify angles based on their measures? | |
Ans. Angles can be classified based on their measures as follows:
- Acute Angle: An angle that measures less than 90 degrees.
- Right Angle: An angle that measures exactly 90 degrees.
- Obtuse Angle: An angle that measures more than 90 degrees but less than 180 degrees.
- Straight Angle: An angle that measures exactly 180 degrees.
| 3. What are the different types of angles based on their relationships with each other? | |
Ans. There are several types of angles based on their relationships with each other:
- Adjacent Angles: Angles that share a common vertex and a common side but do not overlap.
- Vertical Angles: Pairs of opposite angles formed by two intersecting lines. They have equal measures.
- Supplementary Angles: Two angles whose measures add up to 180 degrees.
- Complementary Angles: Two angles whose measures add up to 90 degrees.
| 4. How can lines be classified based on their relationships with each other? | |
Ans. Lines can be classified based on their relationships with each other as follows:
- Parallel Lines: Lines that are always the same distance apart and never intersect.
- Intersecting Lines: Lines that cross each other at a point.
- Perpendicular Lines: Lines that intersect at a right angle (90 degrees).
- Skew Lines: Lines that are not in the same plane and do not intersect.
| 5. How can we find the measure of an unknown angle using the given information about other angles? | |
Ans. The measure of an unknown angle can be found using the given information about other angles by applying various angle relationships and properties. Some common methods include using the properties of supplementary angles, complementary angles, or vertically opposite angles. Additionally, the properties of parallel lines and transversals can also be used to find unknown angle measures.
About this Document
|
1.9K Views |
|
4.89/5 Rating |
|
Nov 22, 2024 Last updated |
Document Description: RS Aggarwal Solutions: Lines and Angles- 1 for Class 9 2024 is part of Mathematics (Maths) Class 9 preparation.
The notes and questions for RS Aggarwal Solutions: Lines and Angles- 1 have been prepared according to the Class 9 exam syllabus. Information about RS Aggarwal Solutions: Lines and Angles- 1 covers topics
like and RS Aggarwal Solutions: Lines and Angles- 1 Example, for Class 9 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises and tests below for RS Aggarwal Solutions: Lines and Angles- 1.
Introduction of RS Aggarwal Solutions: Lines and Angles- 1 in English is available as part of our Mathematics (Maths) Class 9
for Class 9 & RS Aggarwal Solutions: Lines and Angles- 1 in Hindi for Mathematics (Maths) Class 9 course.
Download more important topics related with notes, lectures and mock test series for Class 9
Exam by signing up for free. Class 9: RS Aggarwal Solutions: Lines and Angles- 1 | Mathematics (Maths) Class 9
Description
Full syllabus notes, lecture & questions for RS Aggarwal Solutions: Lines and Angles- 1 | Mathematics (Maths) Class 9 - Class 9 | Plus excerises question with solution to help you revise complete syllabus for Mathematics (Maths) Class 9 | Best notes, free PDF download
Information about RS Aggarwal Solutions: Lines and Angles- 1
In this doc you can find the meaning of RS Aggarwal Solutions: Lines and Angles- 1 defined & explained in the simplest way possible. Besides explaining types of
RS Aggarwal Solutions: Lines and Angles- 1 theory, EduRev gives you an ample number of questions to practice RS Aggarwal Solutions: Lines and Angles- 1 tests, examples and also practice Class 9
tests
|
Explore Courses for Class 9 exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
Related Searches
shortcuts and tricks
,Previous Year Questions with Solutions
,video lectures
,RS Aggarwal Solutions: Lines and Angles- 1 | Mathematics (Maths) Class 9
,mock tests for examination
,past year papers
,Viva Questions
,Summary
,RS Aggarwal Solutions: Lines and Angles- 1 | Mathematics (Maths) Class 9
,practice quizzes
,study material
,Exam
,Semester Notes
,Sample Paper
,Important questions
,Extra Questions
,ppt
,MCQs
,RS Aggarwal Solutions: Lines and Angles- 1 | Mathematics (Maths) Class 9
,Objective type Questions
,Free
;
Additional Information about RS Aggarwal Solutions: Lines and Angles- 1 for Class 9 Preparation
RS Aggarwal Solutions: Lines and Angles- 1 Free PDF Download
The RS Aggarwal Solutions: Lines and Angles- 1 is an invaluable resource that delves deep into the core of the Class 9 exam.
These study notes are curated by experts and cover all the essential topics and concepts, making your preparation more efficient and effective.
With the help of these notes, you can grasp complex subjects quickly, revise important points easily,
and reinforce your understanding of key concepts. The study notes are presented in a concise and easy-to-understand manner,
allowing you to optimize your learning process. Whether you're looking for best-recommended books, sample papers, study material,
or toppers' notes, this PDF has got you covered. Download the RS Aggarwal Solutions: Lines and Angles- 1 now and kickstart your journey towards success in the Class 9 exam.
Importance of RS Aggarwal Solutions: Lines and Angles- 1
The importance of RS Aggarwal Solutions: Lines and Angles- 1 cannot be overstated, especially for Class 9 aspirants.
This document holds the key to success in the Class 9 exam.
It offers a detailed understanding of the concept, providing invaluable insights into the topic.
By knowing the concepts well in advance, students can plan their preparation effectively.
Utilize this indispensable guide for a well-rounded preparation and achieve your desired results.
RS Aggarwal Solutions: Lines and Angles- 1 Notes
RS Aggarwal Solutions: Lines and Angles- 1 Notes offer in-depth insights into the specific topic to help you master it with ease.
This comprehensive document covers all aspects related to RS Aggarwal Solutions: Lines and Angles- 1.
It includes detailed information about the exam syllabus, recommended books, and study materials for a well-rounded preparation.
Practice papers and question papers enable you to assess your progress effectively.
Additionally, the paper analysis provides valuable tips for tackling the exam strategically.
Access to Toppers' notes gives you an edge in understanding complex concepts.
Whether you're a beginner or aiming for advanced proficiency, RS Aggarwal Solutions: Lines and Angles- 1 Notes on EduRev are your ultimate resource for success.
RS Aggarwal Solutions: Lines and Angles- 1 Class 9 Questions
The "RS Aggarwal Solutions: Lines and Angles- 1 Class 9 Questions" guide is a valuable resource for all aspiring students preparing for the
Class 9 exam. It focuses on providing a wide range of practice questions to help students gauge
their understanding of the exam topics. These questions cover the entire syllabus, ensuring comprehensive preparation.
The guide includes previous years' question papers for students to familiarize themselves with the exam's format and difficulty level.
Additionally, it offers subject-specific question banks, allowing students to focus on weak areas and improve their performance.
Study RS Aggarwal Solutions: Lines and Angles- 1 on the App
Students of Class 9 can study RS Aggarwal Solutions: Lines and Angles- 1 alongwith tests & analysis from the EduRev app,
which will help them while preparing for their exam. Apart from the RS Aggarwal Solutions: Lines and Angles- 1,
students can also utilize the EduRev App for other study materials such as previous year question papers, syllabus, important questions, etc.
The EduRev App will make your learning easier as you can access it from anywhere you want.
The content of RS Aggarwal Solutions: Lines and Angles- 1 is prepared as per the latest Class 9 syllabus.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up
within 7 days!
within 7 days!
Takes less than 10 seconds to signup