In ∆ABC, ∠BAC = 60°, and O is a point inside ∆ABC. If ∠OBC is two times ∠OBA and ∠OCB is two times ∠OCA, then what will be the measure of ∠BOC?

Correct option is D

Given:

In  $$\triangle ABC , \angle BAC = 60^\circ$$​​

O  is a point inside  $$\triangle ABC$$​​

$$\angle OBC = 2 \times \angle OBA \\ \ \\ \angle OCB = 2 \times \angle OCA$$​

Solution: 

in $$\triangle ABC$$​

y + 2y + x + 2x = 180 - 60 = 120

3y +3x = 120 

3(x +y) = 120 

x + y = 40  

2y +2x = 2(x + y) = 2 $$\times$$ 40 = 80 

in $$\triangle$$BOC

$$\angle B + \angle C = 80$$ 

Then $$\angle O = 180 -(\angle B+ \angle C)$$ 

= 180 - 80 

= 100