Question

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

(A) 65° 

(B) 130° 

(C) 295° 

(D) 230°

Answer 1

(D) 230°

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

∴ m(arc AB) = 2 m∠ACB 

= 2 × 65 

= 130° 

m(arc ACB) = 360° – m(arc AB) [Measure of a circle is 360°] 

= 360° – 130° 

= 230°