In the diagram, 0 is the centre of the circle. Find the value x

In the diagram, 0 is the centre of the circle. Find the value x

A.

34

B.

29

C.

17

D.

14

Correct answer is D

POQ in a straight line

Hence, < POQ + < QOR = 180o

56o + < QOR = 180o

< QOR = 180o - 56o

= 124o

Now, in \(\bigtriangleup\) QOR OR = OQ = Radius

< ORQ = < OQR = 2x (Base angles of an Isosceles \(\bigtriangleup\))

2x + 124 + 2x = 180o

4x + 124 = 180

4x = 180 - 124

4x = 56

x = \(\frac{56}{4}\)

x = 14o