Question

A, B and C are the three points on a circle such that ∠ABC = 35° and ∠BAC = 85°. What is the angle (in degrees) subtended by arc AB at the centre of the circle?

• A. 60
• B. 90
• C. 135
• D. 120

Answer 1

Answer:

D. 120

In triangle ABC,

∠A + ∠B + ∠C = 180 (angle sum property) 

∠C = 180 - ∠A - ∠B = 180° – 35° – 85° = 60°

∠ AOB = 2∠ACB (Angle subtended at centre is twice that on circle)

∠AOB = 2 × 60° = 120°