Using the inscribed angle theorems, the measure of the indicated angles are:
1. m∠BOA = 30°
2. m∠BDA = 15°
3. m∠BCA = 15°
What is the Inscribed Angle Theorems?
Based on the inscribed angle theorems, the following relationships are established:
- Inscribed angle = 2(measure of intersected arc)
- Central angle = measure of intersected arc
Given:
Intercepted arc BA = 30°
1. ∠BOA is central angle
Thus:
m∠BOA = 30° (inscribed angle theorems)
2. ∠BDA is inscribed angle.
m∠BDA = 1/2(30) = 15° (inscribed angle theorems)
3. m∠BCA = m∠BDA = 15° (inscribed angle theorems)
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