In the diagram, /MN/, /OP/, /QOP/ = 125o. What is the size of < MQR?
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Correct Answer: Option B
Explanation:
< 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
< 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