### Lines and Angles - Solutions

CBSE Class 9 Mathematics

NCERT Solutions

CHAPTER 6

Lines and Angles(Ex. 6.1)

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 .

Reflex

(Vertically opposite angles), or

But, we are given that

Therefore, we can conclude that and .

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 2*x* and *b* be equal to *3x*.

Therefore

Now [Linear pair]

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 thatform 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.

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.

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 thatform 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 thatform 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.

6. It is given thatand 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 thatform 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