Explanation

By the alternate-segment (tangent-chord) theorem, ∠QPT=36° equals the angle subtended by chord PQ in the opposite arc. The central angle subtending the same chord is twice that: ∠POQ=2×36°=72°, option C. Halving instead of doubling gives 18° (not an option), while 36° — the inscribed angle itself — is the intended trap.