Question on: WAEC Mathematics - 1998

Here's how to solve the problem:

1. Visualize: Imagine the circle with chords PQ and RS intersecting at right angles.

2. Angles in a Triangle: Since PQ and RS intersect at a point inside the circle at right angles, we know that ∠QPR is an angle in a triangle formed by the intersection point and points P and Q. The angle at the intersection is 90 degrees. Therefore, the sum of all angles in that triangle will be 180 degrees.

3. Deduce Angle Q: Let's denote the intersection point as "X". Triangle PXQ has angles ∠QPR = 35 degrees, ∠PXQ = 90 degrees, and ∠PQS. Therefore: ∠PQS = 180 - (90 + 35) = 55 degrees.

   However, we need to find ∠PQS. We know that ∠QPR and ∠RSQ subtend the same arc (QR). Therefore, ∠PQS = 35 degrees.