WAEC Mathematics 2017 Theory — Question 16

Model answer

(i) The student draws a circle with tangent PQ touching at S, and the straight line PRT crossing through the circle, marking ∠TPS=34° and ∠TSQ=65° (no diagram is pre-supplied for this part — it must be constructed from the given description). (ii)(A) ∠PST+∠TSQ=180° (angles on a straight line), so ∠PST=180-65=115°. Also ∠PST+∠TPS+∠RTS=180° (sum of angles in a triangle), so ∠RTS=180-(115+34)=31°. (B) ∠TSQ=∠SRT=65° (angles in alternate segment are equal). Since ∠SRP is on a straight line with ∠SRT: ∠SRP=180-∠SRT=180-65=115°.