Question

12(a). In the diagram, PQRS is a circle, |PQ|=|PR|, ∠SPR=26° and the interior angles of ΔPQS are in the ratio 2:3:3. Calculate: (i) ∠POR; (ii) ∠RPQ; (iii) ∠PRQ.

Accepted Answer

Sum of ratio parts = 8. ∠PQS = (2/8)×180° = 45°; ∠PSQ=∠SPQ = (3/8)×180° = 67.5°. Since |PQ|=|PR|, ∠SQR=∠SPR=26° (base angles / alternate segment relation), so ∠PQR=∠PQS+∠SQR=45°+26°=71°=(i) related to ∠POR by the centre-circumference angle relation.
(ii) ∠RPQ = ∠PSQ − ∠SPR = 67.5° − 26° = 41.5°.
(iii) ∠PRQ = 180° − ∠PQR − ∠RPQ = 180° − 71° − 41.5° = 67.5°.

WAEC Mathematics 2021 Theory — Question 19

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