Question

In the given figure, O is the centre of a circle in which $\angle OBA={20}^{\circ }and\angle OCA={30}^{\circ }.\text{Then,}\angle BOC=?$

(a) ${50}^{\circ }$

(b) ${90}^{\circ }$

(c) ${100}^{\circ }$

(d) ${130}^{\circ }$

Answer 1

ANSWER:
( c ) 100°
In Δ OAB, we have:
OA = OB
(Radii of a circle)
⇒ ∠OAB = ∠OBA = 20°
In ΔOAC, we have:
OA = OC
(Radii of a circle)
⇒ ∠OAC = ∠OCA = 30°
Now, ∠BAC = (20° + 30°) = 50°
∴ ∠BOC = (2 × ∠BAC) = (2 × 50 °) = 100°