Question

In the given figure, ray OS stand on a line POQ, Ray OR and ray OT are angle bisectors of ∠POS and∠SOQ respectively. If ∠POS = x, find ∠ROT.

Answer 1

In the figure given below, we have

Rayas the bisector of

Therefore,

Or,

(I)

Similarly, Rayas the bisector of

Therefore,

Or,

(II)

Also, Raystand on a line. Therefore,and form a linear pair.

Thus,

From (I) and (II):

Hence, the value of is 90°.