Answer:
measure of ∠BDC = 30° (option C)
Step-by-step explanation:
Given:
A circle with measure of arc BC = 60°
To find:
measure of ∠BDC
From the diagram, arc BC is common to m∠BAC and m∠BDC
This means the central angle of ∠BAC is the same as the central angle of ∠BDC
To find the angle of BDC, we will apply the theorem:
central angle = 2(inscribed angle)
The Central angle is represented by arc BC = 60°
inscribed angle = ∠BDC
![\begin{gathered} 60\text{ = 2\lparen\angle BDC\rparen} \\ (60)/(2)\text{ = \angle BDC} \\ \\ ∠BDC=\text{ 30\degree \lparen option C\rparen} \end{gathered}]()