Question

In the given figure, O is centre of the circle. OQ and OR are the angle bisectors of /_Q and /_R respectively. If QR is extended to S, then /_PRS will be ???

anyone can help me with this with proper solution please!!!​

Answer 1

(1) 120°

Explanation:

QOR is one-third of the the circle which angle at O is 120°.

Since the angles at Q and R have been bisected, then their angles are two times the bisected angle

`q = r = 60 \\ 120 = 2r \\ 120= 60`

Since two angles are 60° each, then triangle PQR is an equilateral triangle.

sum of interior opposite angles= exterior angle

`e = 60 + 60 \\ e = 120`

Therefore the angle PRS is 120°

Also when you look at the angle closely, you would see the it is beyond right angle and all the other angles in the options which make 120° obviously the answer.