WAEC Mathematics 2015 Theory — Question 6
Question 6 of 22 from the West African Examinations Council (WAEC) Mathematics 2015 Theory paper, with the correct answer and a full explanation.
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3(b). The diagram shows a circle PQRS with centre O, ∠UQR=68°, ∠TPS=74° and ∠QSR=40°. Calculate the value of ∠PRS.
Model answer
∠PRQ = 68−40 = 28° (exterior angle of cyclic quadrilateral = sum of opposite interior angles). ∠RSQ = ∠RPQ = 40° (angles in the same segment). ∠TPS = ∠PRS+∠PRQ (exterior angle of cyclic quadrilateral), so ∠PRS = 74−28 = 46°.
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