In the given figure, OB and OC are the bisectors of ∠AOD and ∠BOD respectively and ∠BOA = 30°. Then find the measure of ∠DOC.

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Solution

Given: ∠BOA = 30°
∴ ∠BOD = 30° (∵ OB bisects ∠AOD)
Also, OC bisects ∠BOD.
$∴ ∠ B O C = ∠ D O C = \frac{∠ B O D}{2}$
$\Rightarrow ∠ B O C = ∠ D O C = \frac{30^{\circ}}{2} = 15^{\circ}$
∴ ∠DOC = 15°

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