NCERT Solutions for Class 9 Maths Unit 6

Lines and Angles Class 9

Unit 6 Lines and Angles Exercise 6.1, 6.2, 6.3 Solutions

Line
A line is a collection of points that extends without limit in a straight formation. A line can be named by a single letter, like line l, or it can be named according to two points that it contains, like line AB. The second way of naming a line indicates an important property common to all lines: any two points in space determine a line.

Angles
Technically speaking, an angle is the union of two rays (lines that extend infinitely in just one direction) that share an endpoint (called the vertex of the angle). The measure of an angle is how far you must rotate one of the rays such that it coincides with the other.
<< Previous Chapter 5 : Introduction to Euclid's Geometry Next Chapter 7 : Triangles >>

Exercise 6.1 : Solutions of Questions on Page Number : 96

Q1 :  

In the given figure, lines AB and CD intersect at O. If and find ∠BOE and reflex ∠COE.


Answer :

Answer needs Correction? Click Here

Q2 :  

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


Answer :

Let the common ratio between a and b be x.

a = 2x, and b = 3x

XY is a straight line, rays OM and OP stand on it.

∴ ∠ XOM + ∠ MOP + ∠ POY = 180º

b + a + ∠ POY = 180º

3x + 2x + 90º = 180º

5x = 90º

x = 18º

a = 2x = 2 x 18 = 36º

b = 3x= 3 x 18 = 54º

MN is a straight line. Ray OX stands on it.

b + c = 180º (Linear Pair)

54º + c = 180º

c = 180º - 54º = 126º

c = 126º

Answer needs Correction? Click Here

Q3 :  

In the given figure, ∠ PQR = ∠ PRQ, then prove that ∠ PQS = ∠ PRT.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

In the given figure, if then prove that AOB is a line.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

In the given figure, POQ is a line. Ray OR is perpendicular to line PQ. OS is another ray lying between rays OP and OR. Prove that


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

It is given that ∠XYZ = and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects ∠ZYP, find ∠XYQ and reflex ∠QYP.


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 5 : Introduction to Euclid's Geometry Next Chapter 7 : Triangles >>

Exercise 6.2 : Solutions of Questions on Page Number : 103

Q1 :  

In the given figure, find the values of x and y and then show that AB || CD.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

In the given figure, if AB || CD, CD || EF and y: z = 3: 7, find x.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

In the given figure, If AB || CD, EF ⊥ CD and ∠ GED = 126º, find ∠ AGE, ∠ GEF and ∠ FGE.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

In the given figure, if PQ || ST, ∠ PQR = 110º and ∠ RST = 130º, find ∠ QRS.

[Hint: Draw a line parallel to ST through point R.]


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

In the given figure, if AB || CD, ∠ APQ = 50º and ∠ PRD = 127º, find x and y.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

In the given figure, PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB || CD.


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 5 : Introduction to Euclid's Geometry Next Chapter 7 : Triangles >>

Exercise 6.3 : Solutions of Questions on Page Number : 107

Q1 :  

In the given figure, sides QP and RQ of ΔPQR are produced to points S and T respectively. If ∠ SPR = 135º and ∠ PQT = 110º, find ∠ PRQ.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q2 :  

In the given figure, ∠ X = 62º, ∠ XYZ = 54º. If YO and ZO are the bisectors of ∠ XYZ and ∠ XZY respectively of ΔXYZ, find ∠ OZY and ∠ YOZ.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q3 :  

In the given figure, if AB || DE, ∠ BAC = 35º and ∠ CDE = 53º, find ∠ DCE.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q4 :  

In the given figure, if lines PQ and RS intersect at point T, such that ∠ PRT = 40º, ∠ RPT = 95º and ∠ TSQ = 75º, find ∠ SQT.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q5 :  

In the given figure, if PQ ⊥ PS, PQ || SR, ∠ SQR = 28º and ∠ QRT = 65º, then find the values of x and y.


Answer :

Please Register/Login to get access to all solutions Facebook Login
Q6 :  

In the given figure, the side QR of ΔPQR is produced to a point S. If the bisectors of ∠PQR and ∠PRS meet at point T, then prove that ∠QTR=∠QPR.


Answer :

Please Register/Login to get access to all solutions Facebook Login
<< Previous Chapter 5 : Introduction to Euclid's Geometry Next Chapter 7 : Triangles >>

Maths : CBSE NCERT Exercise Solutions for Class 9th for Lines and Angles ( Exercise 6.1, 6.2, 6.3 ) will be available online in PDF book form soon. The solutions are absolutely Free. Soon you will be able to download the solutions.

Popular Articles