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WAEC Mathematics 2013 Paper

Question : 47

Total: 48

Solution:

Concept:

Use parallel-line angle properties and the angle sum of a triangle.

Explanation:

Reflex

\angle SRQ = 198^\circ

, so the interior angle at

R

is:

\angle SRQ = 360^\circ - 198^\circ = 162^\circ

Since

ST \parallel PQ

, the angle formed by the transversal

TQ

with

ST

is equal to

\angle RQP = 72^\circ

Therefore, on the straight line at

T

\angle STR = 180^\circ - 72^\circ = 108^\circ

Because

R

lies on the straight line

TQ

, the rays

RQ

and

RT

are opposite rays.

Hence,

\angle SRT = 180^\circ - \angle SRQ = 180^\circ - 162^\circ = 18^\circ

In triangle

SRT

y + 108^\circ + 18^\circ = 180^\circ

y = 180^\circ - 126^\circ = 54^\circ

Answer:

y = 54^\circ

(Option B).

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