Question

In the given figure, OD and OB are the bisectors of ∠EOC and ∠COA respectively. The measure of ∠DOB is equal to

• A. 40°
• B. 30°
• C. 45°
• D. 50°

Answer 1

The correct option is C 45°

Since EO ⊥ OA and OC is bisector of ∠EOA.
∴ ∠EOC = ∠COA = 45°
Now, OD and OB bisects ∠EOC and ∠COA respectively.
$\therefore \angle DOC=\frac{{45}^{\circ }}{2}={22.5}^{\circ }$ and $\angle BOC=\frac{{45}^{\circ }}{2}={22.5}^{\circ }$
$\Rightarrow \angle DOB=\angle DOC+\angle BOC$
= 22.5° + 22.5°
= 45°
Hence, the correct answer is option (c).