A triangle PQR is inscribed in a circle centred at O. A tangent PT at P is drawn such that ∠QPT = 36°, then ∠POQ is equal to

By the tangent-chord angle theorem, the angle between tangent PT and chord PQ equals the inscribed angle in the alternate segment, which is ∠PRQ. So ∠PRQ = 36°. The central angle ∠POQ subtending the same arc PQ is twice the inscribed angle: ∠POQ = 2·∠PRQ = 2·36° = 72°.