Question

In the given figure, O is the centre of a circle and $\angle AOC={120}^{\circ }.$ Then, $\angle$BDC = ?

(a) ${60}^{\circ }$

(b) ${45}^{\circ }$

(c) ${30}^{\circ }$

(d) ${15}^{\circ }$

Answer 1

ANSWER:
( c ) 30°
∠COB = 180° - 120° = 60° (Linear pair)
Now, arc BC subtends ∠COB at the centre and ∠BDC at the point D of the remaining part of the circle.
∴ ∠COB = 2∠BDC
⇒ ∠BDC=1/2∠COB=1/2×60°=30°