18Inscribed angle theorem

Points A, B and C lie on a circle with centre O. The central angle ∠AOB is 110°. Find the inscribed angle ∠ACB, where C is on the major arc.

The inscribed angle ∠ACB is 55°, since an inscribed angle is always half the central angle on the same arc. From ∠AOB = 2·∠ACB, 110 = 2·∠ACB gives ∠ACB = 55°. Check: 2×55° = 110° ✓.