Exercise 6.3
NCERT solutions for Class 9 Maths Lines and Angles
NCERT Solutions for Class 9 Mathematics Lines and Angles
1. In the given figure, sides QP and RQ of ∆PQR are produced to points S and T respectively. If 
SPR = 135º and PQT = 110º, find PRQ.
Ans. We are given that
and 
.
We need to find the value of
in the figure given below.
From the figure, we can conclude that
form a linear pair.
We know that the sum of angles of a linear pair is
.
and 
and 
Or, 
From the figure, we can conclude that
(Angle sum property)
Therefore, we can conclude that
.
NCERT Solutions for Class 9 Maths Exercise 6.3
2. In the given figure, X = 62º, XYZ = 54º. If YO and ZO are the bisectors of XYZ and XZY respectively of ∆XYZ, find OZY and YOZ.
Ans. We are given that
and YO and ZO are bisectors of
, respectively.
We need to find
in the figure.
From the figure, we can conclude that in
(Angle sum property)
We are given that OY and OZ are the bisectors of, respectively.
and 
From the figure, we can conclude that in
(Angle sum property)
Therefore, we can conclude that
and
.
NCERT Solutions for Class 9 Maths Exercise 6.3
3. In the given figure, if AB || DE, BAC = 35º and CDE = 53º, find DCE.
Ans. We are given that
,
.
We need to find the value of
in the figure given below.
From the figure, we can conclude that
(Alternate interior)
From the figure, we can conclude that in
(Angle sum property)
Therefore, we can conclude that
.
NCERT Solutions for Class 9 Maths Exercise 6.3
4. In the given figure, if lines PQ and RS intersect at point T, such that PRT = 40º, RPT = 95º and TSQ = 75º, find SQT.
Ans. We are given that
.
We need to find the value of
in the figure.
From the figure, we can conclude that in
(Angle sum property)
From the figure, we can conclude that
(Vertically opposite angles)
From the figure, we can conclude that in
(Angle sum property)
Therefore, we can conclude that
.
NCERT Solutions for Class 9 Maths Exercise 6.3
5. In the given figure, if
, PQ || SR,
, then find the values of x and y.
Ans. We are given that
.
We need to find the values of x and y in the figure.
We know that “If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.”
From the figure, we can conclude that
, or
From the figure, we can conclude that
(Alternate interior angles)
From the figure, we can conclude that
(Angle sum property)
Therefore, we can conclude that
.
NCERT Solutions for Class 9 Maths Exercise 6.3
6. In the given figure, the side QR of ∆PQR is produced to a point S. If the bisectors of
meet at point T, then prove that
.
Ans. We need to prove thatin the figure given below.
We know that “If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.”
From the figure, we can conclude that in
,
is an exterior angle
…(i)
From the figure, we can conclude that in,is an exterior angle
We are given that 
are angle bisectors of 
We need to substitute equation (i) in the above equation, to get
Therefore, we can conclude that the desired result is proved.