SSC CGL 16 Aug 2015 Shift 2 Paper

∠ OBC = $\frac{1}{2}$ ∠ ABC ;
∠ OCB = $\frac{1}{2}$ ∠ ACB
From Δ OBC,
∠ OBC + ∠ OCB + ∠ BOC = 180°
$\frac{1}{2}$ (∠ ABC + ∠ ACB) + ∠ BOC = 180°
⇒ $\frac{1}{2}$ (180° - ∠ BAC) + ∠ BOC = 180°
⇒ $\frac{1}{2}$ (180° - 100°) + ∠ BOC = 180°
⇒ ∠ BOC = $180°-40°$ = 140°