Exercise 6.1
NCERT solutions for Class 9 Maths Lines and Angles
NCERT Solutions for Class 9 Mathematics Lines and Angles
1. In Fig. 6.13, lines AB and CD intersect at O. If 
and
, find 
and reflex
.
Ans. We are given that
and
.
We need to find
.
From the given figure, we can conclude that
form a linear pair.
We know that sum of the angles of a linear pair is
.
or
Reflex 
(Vertically opposite angles), or
But, we are given that
Therefore, we can conclude that
and
.
NCERT Solutions for Class 9 Maths Exercise 6.1
2. In Fig. 6.14, lines XY and MN intersect at O. If 
and a:b = 2 : 3, find c.
Ans. We are given that
and
.
We need find the value of c in the given figure.
Let a be equal to 2x and b be equal to 3x.
Therefore
Now
[Linear pair]
NCERT Solutions for Class 9 Maths Exercise 6.1
3. In the given figure,
, then prove that 
.
Ans. We need to prove that.
We are given that.
From the given figure, we can conclude that
form a linear pair.
We know that sum of the angles of a linear pair is.
and (i)
(ii)
From equations (i) and (ii), we can conclude that
Therefore, the desired result is proved.
NCERT Solutions for Class 9 Maths Exercise 6.1
4. In Fig. 6.16, if x + y = w + z, then prove that AOB is a line.
Ans. We need to prove that AOB is a line.
We are given that
.
We know that the sum of all the angles around a fixed point is
.
Thus, we can conclude that
But, (Given).
From the given figure, we can conclude that y and x form a linear pair.
We know that if a ray stands on a straight line, then the sum of the angles of linear pair formed by the ray with respect to the line is.
.
Therefore, we can conclude that AOB is a line.
NCERT Solutions for Class 9 Maths Exercise 6.1
5. 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
Ans. We need to prove that
.
We are given that OR is perpendicular to PQ, or
From the given figure, we can conclude that
form a linear pair.
We know that sum of the angles of a linear pair is.
, or
.
From the figure, we can conclude that
.
, or
.(i)
From the given figure, we can conclude that
form a linear pair.
We know that sum of the angles of a linear pair is.
, or
.(ii)
Substitute (ii) in (i), to get
Therefore, the desired result is proved.
NCERT Solutions for Class 9 Maths Exercise 6.1
6. It is given that
and XY is produced to point P. Draw a figure from the given information. If ray YQ bisects
, find 
Ans. We are given that, XY is produced to P and YQ bisects.
We can conclude the given below figure for the given situation:
We need to find.
From the given figure, we can conclude that
form a linear pair.
We know that sum of the angles of a linear pair is.
.
But.
Ray YQ bisects, or
.
Reflex 
Therefore, we can conclude that
and Reflex 