Question

∠ACB is inscribed in arc ACB of a circle with centre O. If ∠ACB = 65°, find m(arc ACB).

Options

• 65°

• 130°

• 295°

• 230°

Answer 1

230°

Explanation:

`∠ACB = 1/2 m(arc  AB)`   ...[Inscribed angle theorem]

∴ `65^circ = 1/2 m(arc  AB)`

∴ m(arc AB) = 130°

∴ m(arc ACB) = 360° – m(arc AB)

= 360° – 130°

= 230°