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


Question

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

Options

A) 11o

B) 120o

C) 130o

D) 160o

The correct answer is B.

Explanation:

< NOP = 180 - 125 = 55\(^{\circ}\)(< s on a straight line)
But < NOP = < ONM (alternate < s)
< ONM = 55\(^{\circ}\)
< M + < N + < MQN = 180\(^{\circ}\) (sum of interior < s of a \(\bigtriangleup\)) i.e
65\(^{\circ}\) + 55\(^{\circ}\) + < MQN = 180
< MQN = 180 - 120 = 60
< MQR + < MQN = 180 (< s on straight line)
< MQR + 60 = 180
< MQR + 60 = 180
< MQR = 180 - 60
= 120\(^{\circ}\)

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Dicussion (1)

  • < NOP = 180 - 125 = 55\(^{\circ}\)(< s on a straight line)
    But < NOP = < ONM (alternate < s)
    < ONM = 55\(^{\circ}\)
    < M + < N + < MQN = 180\(^{\circ}\) (sum of interior < s of a \(\bigtriangleup\)) i.e
    65\(^{\circ}\) + 55\(^{\circ}\) + < MQN = 180
    < MQN = 180 - 120 = 60
    < MQR + < MQN = 180 (< s on straight line)
    < MQR + 60 = 180
    < MQR + 60 = 180
    < MQR = 180 - 60
    = 120\(^{\circ}\)

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