In the diagram, /MN/, /OP/, /QOP/ = 125o. What is the size of < MQR?

In the diagram, /MN/, /OP/, /QOP/ = 125o. What is the size of < MQR?

A.

11o

B.

120o

C.

130o

D.

160o

Correct answer is B

< NOP = 180 - 125 = 55o(< s on a straight line)

But < NOP = < ONM (alternate < s)

< ONM = 55o

< M + < N + < MQN = 180o (sum of interior < s of a \(\bigtriangleup\)) i.e

65o + 55o + < MQN = 180

< MQN = 180 - 12o = 60

< MQR + < MQN = 180 (< s on straight line)

< MQR + 60 = 180

< MQR + 60 = 180

< MQR = 180 - 60

= 120o