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WAEC Mathematics 2012 Paper

Question : 44

Total: 49

Solution:

Concept:

Use the angle-sum property of triangles and the alternate interior angles formed by parallel lines.

Explanation:

\triangle NOP

, the angles at

N

and

O

are

129^\circ

and

37^\circ

Thus,

\angle NPO = 180^\circ - (129^\circ + 37^\circ) = 14^\circ

Since

MN \parallel PO

and

PN

is a transversal, alternate interior angles are equal.

So,

\angle MNP = \angle NPO = 14^\circ

Now in

\triangle MNP

, we have

\angle PMN = 112^\circ

and

\angle MNP = 14^\circ

Using the angle-sum property of a triangle,

y = \angle MPN = 180^\circ - (112^\circ + 14^\circ) = 54^\circ

Answer:

y = 54^\circ

Correct option: B.

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