Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Class 9 Mathematics by Full Circle

Created by: Full Circle

Class 9 : Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

The document Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev is a part of the Class 9 Course Class 9 Mathematics by Full Circle.
All you need of Class 9 at this link: Class 9

Question 1. In the following figure, lines AB and CD intersect at O. If ∠AOC + ∠BOE = 70º and ∠BOD = 40º, find ∠BOE and reflex ∠COE.

Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Solution: Since AB is a straight line,
∴ ∠AOC + ∠COE + ∠EOB = 180°
or (∠AOC + ∠BOE) + ∠COE = 180º
or 70º + ∠COE = 180º                [∵ ∠AOC + ∠BOC = 70º (Given)]
or ∠COE = 180º - 70º = 110º

∴ Reflex ∠COE = 360º - 110º = 250º
∵ AB and CD intersect at O.
∴ ∠COA = ∠BOD                  [Vertically opposite angles]
But ∠BOD = 40º [Given]
∴ ∠COA = 40º
Also ∠AOC + ∠BOE = 70°
∴  40º + ∠BOE = 70º
or ∠BOE = 70º ∠ 40º = 30º
Thus, ∠BOE = 30º and reflex ∠COE = 250.
 

Question 2. In the following figure, lines XY and MN intersect at O. If ∠POY = 90º and a : b = 2 : 3, find c.

Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Solution: ∵ XOY is a straight line.
∴ ∠b + ∠a + ∠POY = 180º
But ∠OPY = 90º                      [Given]
∴ ∠b + ∠a = 180º ∠ 90º = 90º.
Also a : b = 2 : 3

∴   Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Since XY and MN intersect at O,
∴ ∠ c= [∠a + ∠POY]                                      [Vertically opposite angles]
or ∠ c = 36º + 90º = 126º
Thus, the required measure of ‘c’ = 126º.
 

Question 3. In the following figure, ∠PQR = ∠PRQ, then prove that ∠PQS = ∠PRT.

Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Solution: ∵ ST is a straight line,
∴ ∠PQS + ∠PQR = 180º               ...(1)
Similarly, ∠PRT + ∠PRQ = 180º   ...(2)
From (1) and (2), we have
∠PQS + ∠PQR = ∠PRT + ∠PRQ

But ∠PQR = ∠PRQ              [Given]
∴ ∠PQS = ∠PRT
 

Question 4. In the following figure, if x + y = w + z, then prove that AOB is a line.

Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

Solution: ∵ Sum of all the angles at a point = 360º
∴ x + y + z + w = 360º
or (x + y) + (z + w) = 360º
But (x + y) = (z + w) [Given]
∴ (x + y) + (x + y) = 360º
or 2(x + y) = 360º
or (x + y) = (360o/2)= 180º
∴ AOB is a straight line.


Question 5. In the adjoining figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that ∠ ROS = (1/2)
 (∠QOS ∠ ∠POS).
 Solution:
∵ POQ is a straight line.                     [Given]
∴ ∠POS + ∠ROS + ∠ROQ = 180º

Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

But OR ⊥ PQ
∴ ∠ROQ = 90º
∴ ∠POS + ∠ROS + 90º = 180º
⇒ ∠POS + ∠ROS = 90º              …(1)
Now, we have ∠ROS + ∠ROQ = ∠QOS
⇒ ∠ROS + 90º = ∠QOS            …(2)
From (1) and (2),
we have ∠ROS + [∠POS + ∠ROS] = ∠QOS
⇒ 2∠ROS + ∠POS = ∠QOS
⇒ 2∠ROS = [∠QOS  ∠POS]
∴  ∠ROS = (1/2)[∠QOS  ∠POS]


Question 6. It is given that ∠XYZ = 64º and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.
 Solution: 
∵ XYP is a straight line.

Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

∴ ∠XYZ + ∠ZYQ + ∠QYP = 180º
⇒ 64º + ∠ZYQ + ∠QYP = 180º            [∵ YQ, bisects ∠ZYP, so ∠QYP = ∠ZYQ]
⇒ 64º + 2∠QYP = 180º
⇒ 2∠QYP = 180º - 64º = 116º
⇒ ∠QYP = (1160/2)= 58º
∴ Reflex ∠QYP = 360º - 58º = 302º
Since ∠XYQ = ∠XYZ + ∠ZYQ
⇒ ∠XYQ = 64º + ∠QYP         [∵ ∠XYZ = 64º (Given) and ∠ZYQ = ∠QYP]
⇒ ∠XYQ = 64º + 58º [∵ ∠QYP = 58º]
= 122º
Thus, ∠XYQ = 122º and reflex ∠QYP = 302°

Share with a friend

Complete Syllabus of Class 9

Dynamic Test

Content Category

Related Searches

MCQs

,

study material

,

Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

,

Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

,

practice quizzes

,

ppt

,

shortcuts and tricks

,

past year papers

,

pdf

,

Sample Paper

,

Important questions

,

Objective type Questions

,

Free

,

Exam

,

Extra Questions

,

Summary

,

video lectures

,

Ex 6.1 NCERT Solutions- Lines and Angles Class 9 Notes | EduRev

,

mock tests for examination

,

Viva Questions

,

Semester Notes

,

Previous Year Questions with Solutions

;