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°