In the diagram, MN//PO, < ∠ PMN = 112°, ∠ PNO = 129° and ∠
MATHEMATICS
WAEC 2012
In the diagram, MN//PO,< ∠ PMN = 112°, ∠ PNO = 129° and ∠ MPN = y°. Find the value of y
- A. 51°
- B. 54°
- C. 56°
- D. 68°
Correct Answer: B. 54°
Explanation
In \(\bigtriangleup\) NPO + PNO + PNO +< NOP = 180o(sum of interior angles of a \(\bigtriangleup\) )
i.e. NPO + 129 + 37 = 180
< NOP = 180 - (129 + 37) = 14o
< MNP =< NOP = 14o (alt.< s)
In \(\bigtriangleup\) MPN
< PMN +< MNP + y = 180(sum of interior angles of a \(\bigtriangleup\))
i.e. 112 + 14 + y = 180o
y = 180 - (112 + 14) = 180 - 126 = 54o
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