Question

the measure of the arc ab is 30 degrees.

1. what is the measure of ∠boa? degrees
2. what is the measure of ∠bda? degrees
3. what is the measure of ∠bca? degrees

Explanation:

Step1: Find the measure of ∠BOA

The measure of a central angle is equal to the measure of its intercepted arc.
Since the measure of arc \(AB\) is \(30^{\circ}\), then \(\angle BOA = 30^{\circ}\)

Step2: Find the measure of ∠BDA

The measure of an inscribed angle is half the measure of its intercepted arc.
For \(\angle BDA\), the intercepted arc is \(AB\). Using the formula \(\angle BDA=\frac{1}{2}\text{measure of arc }AB\)
Substitute the measure of arc \(AB = 30^{\circ}\), so \(\angle BDA=\frac{1}{2}\times30^{\circ}=15^{\circ}\)

Step3: Find the measure of ∠BCA

The measure of an inscribed angle is half the measure of its intercepted arc.
For \(\angle BCA\), the intercepted arc is \(AB\). Using the formula \(\angle BCA=\frac{1}{2}\text{measure of arc }AB\)
Substitute the measure of arc \(AB = 30^{\circ}\), so \(\angle BCA=\frac{1}{2}\times30^{\circ}=15^{\circ}\)

Answer:

1. \(30\)
2. \(15\)
3. \(15\)