A triangle PQR is inscribed in a circle with its centre at O. A tangent PT is drawn at P such that ∠QPT = 36°. What is ∠POQ equal to?

By the tangent-chord angle theorem, the angle between tangent PT and chord PQ equals the inscribed angle in the alternate segment. The angle subtended by chord PQ at the centre is twice the inscribed angle. So ∠POQ = 2 × ∠QPT = 2 × 36° = 72°.