Exercise 6.2
NCERT solutions for Class 9 Maths Lines and Angles
NCERT Solutions for Class 9 Mathematics Lines and Angles
1. In the given figure, find the values of x and y and then show that AB || CD.
Ans. We need to find the value of x and y in the figure given below and then prove that
.
From the figure, we can conclude that
(Vertically opposite angles), and
form a pair of linear pair.
We know that the sum of linear pair of angles is
.
.
From the figure, we can conclude that
form a pair of alternate interior angles corresponding to the lines AB and CD.
Therefore, we can conclude that
.
NCERT Solutions for Class 9 Maths Exercise 6.2
2. In the given figure, if AB || CD, CD || EF and y: z = 3: 7, find x.
Ans. We are given that,
and
.
We need to find the value of x in the figure given below.
We know that lines parallel to the same line are also parallel to each other.
We can conclude that
.
Let
.
We know that angles on same side of a transversal are supplementary.
.
(Alternate interior angles)
Now
Therefore, we can conclude that
.
NCERT Solutions for Class 9 Maths Exercise 6.2
3. In the given figure, If AB || CD,
and
, find
.
Ans. We are given that,and
.
We need to find the value of in the figure given below.
(Alternate angles)
From the given figure, we can conclude that
form a linear pair.
We know that sum of the angles of a linear pair is.
(Alternate interior angles)
Therefore, we can conclude that
and 
.
NCERT Solutions for Class 9 Maths Exercise 6.2
4. In the given figure, if PQ || ST, 
and
, find
.
[Hint: Draw a line parallel to ST through point R.]
Ans. We are given that
,
and
.
We need to find the value of
in the figure.
We need to draw a line RX that is parallel to the line ST, to get
Thus, we have
.
We know that lines parallel to the same line are also parallel to each other.
We can conclude that
.
, or(Alternate interior angles)
.
We know that angles on same side of a transversal are supplementary.
From the figure, we can conclude that
Therefore, we can conclude that
.
NCERT Solutions for Class 9 Maths Exercise 6.2
5. In the given figure, if AB || CD, 
and
, find x and y.
Ans. We are given that
,
and.
We need to find the value of x and y in the figure.
(Alternate interior angles)
(Alternate interior angles)
Therefore, we can conclude that
.
NCERT Solutions for Class 9 Maths Exercise 6.2
6. 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.
Ans. We are given that PQ and RS are two mirrors that are parallel to each other.
We need to prove thatin the figure.
Let us draw lines BX and CY that are parallel to each other, to get
We know that according to the laws of reflection
and 
.
(Alternate interior angles)
We can conclude that
.
From the figure, we can conclude that
and 
Therefore, we can conclude that
.
From the figure, we can conclude that
form a pair of alternate interior angles corresponding to the lines AB and CD, and transversal BC.
Therefore, we can conclude that