Question

In the given figure, OB and OC are the bisectors of ∠AOD and ∠BOD respectively and ∠BOA = 30°. The measure of ∠DOC is equal to

• A.
  20°
• B.
  30°
• C.
  15°
• D.
  $7{\frac{1}{2}}^{\circ }$

Answer 1

The correct option is C

15°
Given: ∠BOA = 30°
∴ ∠BOD = 30° (∵ OB bisects ∠AOD)
Also, OC bisects ∠BOD.
$\therefore \angle BOC=\angle DOC=\frac{\angle BOD}{2}$
$\Rightarrow \angle BOC=\angle DOC=\frac{{30}^{\circ }}{2}={15}^{\circ }$
∴ ∠DOC = 15°
Hence, the correct answer is option (c).