Question

In the diagram below, P and Q are points on a circle with centre O.

PQT is a tangent to the circle.
Angle OPQ=18∘

Work out the size of angle PQT.

Answer 1

∠PQT = 72°

Explanation:

According to the diagram shown, ∠OPQ = ∠OQP = 18°. If PQT is a tangent to the circle, it can be inferred that line OQ is perpendicular to line QT. Ths shows that ∠OQT = 90°.

Also from the diagram, ∠OQP + ∠PQT = ∠OQT;

∠PQT = ∠OQT - ∠OQP

Given ∠OQP = 18° and ∠OQT = 90°

∠PQT = 90°-18°

∠PQT = 72°