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In the diagram, MN//PO, < PMN = 112^o, < PNO = 129...

In the diagram, MN//PO, < PMN = 112o, < PNO = 129o

In the diagram, MN//PO, < PMN = 112^o, < PNO = 129^oo and < MPN = y^o. Find the value of y

A.

51^o

B.

54^o

C.

56^o

D.

68^o

View answer & explanation

Correct answer is B

In $\bigtriangleup$ NPO + PNO + PNO + < NOP = 180^o(sum of interior angles of a $\bigtriangleup$ )

i.e. NPO + 129 + 37 = 180

< NOP = 180 - (129 + 37) = 14^o

< MNP = < NOP = 14^o (alt. < s)

In $\bigtriangleup$ MPN

< PMN + < MNP + y = 180(sum of interior angles of a $\bigtriangleup$ )

i.e. 112 + 14 + y = 180^o

y = 180 - (112 + 14) = 180 - 126 = 54^o

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