Question

Find \( x \) of \( \angle A O C=70^{\circ} \) and \( \angle B A O=50^{\circ} \) where 0 is centre of the circle. (a) \( 35^{\circ} \) (b) \( 30^{\circ} \) (c) \( 25^{\circ} \) (d) \( 15^{\circ} \)

Answer 1

Consider △ABO, 

AO=BO

⇒∠BAO=∠ABO=30⁰

Consider △CBO, 

CO=BO,

⇒∠BCO=∠CBO=40⁰

⇒∠ABC=∠ABO+∠CBO=30⁰+40⁰=70⁰

The angle subtended at the centre is twice the angle subtended anywhere on the arc, 

so,

∠AOC=2×∠ABC=140.⁰

Hope this helps!