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WAEC Mathematics 2024 Paper

Question : 30

Total: 50

In the diagram above, < SQR = 52º and < PRT = 16º. Find the value of the angle marked y

Solution:

Concept:

Use the triangle angle-sum rule and the cyclic quadrilateral angle theorem.

Explanation:

Consider

\triangle QRS

\angle SQR = 52^\circ

and

\angle QRS = 16^\circ

The sum of angles in a triangle is

180^\circ

, so:

52^\circ + 16^\circ + \angle RSQ = 180^\circ

Therefore,

\angle RSQ = 180^\circ - 52^\circ - 16^\circ = 112^\circ

Since

y

is an exterior angle of the cyclic quadrilateral, it equals the interior opposite angle

\angle RSQ

Thus,

y = 112^\circ

Answer:

y = 112^\circ

(Option C).

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