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WAEC Mathematics 2017 Paper

Question : 44

Total: 49

^o

^o

Solution:

Concept:

Use corresponding angles formed by parallel lines and the angle-sum property of a triangle.

Explanation:

From the diagram,

P, R, S

lie on the same straight line, so

\angle TRS = 180^\circ - \angle PRT = 180^\circ - 100^\circ = 80^\circ

\triangle RTS

\angle RTS = 50^\circ

Therefore,

\angle TSR = 180^\circ - (80^\circ + 50^\circ) = 50^\circ

Since

NQ \parallel TS

, corresponding angles are equal, so

\angle QPR = \angle TSR = 50^\circ

At point

P

PN

and

PQ

lie on the same straight line, hence

\angle NPR + \angle QPR = 180^\circ

Thus,

\angle NPR = 180^\circ - 50^\circ = 130^\circ

Answer:

\angle NPR = 130^\circ

(Option B).

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