WAEC Mathematics 2019 Objective — Question 31

Question 31 of 145 from the West African Examinations Council (WAEC) Mathematics 2019 Objective paper, with the correct answer and a full explanation.

31. In the diagram, POS and ROT are straight lines, OPQR is a parallelogram, |OS| = |OT| and ∠OST = 50°. Calculate the value of ∠OPQ.

A. 100°
B. 120°Correct
C. 140°
D. 160°

Explanation

Since |OS|=|OT|, triangle OST is isosceles with base angles equal: ∠OST=∠OTS=50°. So ∠SOT=180−(50+50)=80°. ∠SOT and ∠POR are vertically opposite, so ∠POR=80°. Since OPQR is a parallelogram, ∠PQR=∠POR=80° (opposite angles equal), and the angles in the parallelogram sum to 360°: ∠POR+∠RQP+∠OPQ+∠QRO=360°. Since ∠OPQ=∠ORQ (opposite angles), 80+80+2∠OPQ=360 ⇒ 2∠OPQ=200 ⇒ ∠OPQ=100°. (Working shown in key gives ∠OPQ=100°, corresponding to option A; the key's letter answer is recorded as B—flagged as a possible key inconsistency.)

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