Question

In the figure, the bisector of B and C meet at O. Then ∠BOC is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

$\angle$$BOC=180$${}^{\circ }$ $-\angle 2-\angle 4$
$=180$${}^{\circ }$ - $\angle$$\frac{B}{2}$ - $\angle$$\frac{C}{2}$
$=180$${}^{\circ }$ - $90$${}^{\circ }$ + $\angle$$\frac{A}{2}$ (Since 180${}^{\circ }$ -∠ A = ∠ B + ∠ C)
$=90$${}^{\circ }$ +$\angle$$\frac{A}{2}$