Question

In circle A, Segment BD is a diameter, and the measure of arc CB is 36°:

Points B, C, and D lie on Circle A. Line segment BD is the diameter of circle A; the measure of arc CB is 36 degrees.

What is the measure of ∠DBC?

36°
72°
18°
54°

Answer 1

To find the measure of \(\angle DBC\), we can use the relationship between angles and arcs in a circle.

Given that:

- \(BD\) is the diameter of circle \(A\), it means that angle \(\angle BCD\) will be a right angle (90 degrees), because an angle inscribed in a semicircle is always a right angle.
- The measure of arc \(CB\) is 36 degrees.

Using the fact that the measure of an angle inscribed in a circle is half the measure of the arc that it subtends, we have:

\[
\angle DBC = \frac{1}{2} \times \text{measure of arc CB}
\]

Since the measure of arc \(CB\) is 36 degrees:

\[
\angle DBC = \frac{1}{2} \times 36 = 18 \text{ degrees}
\]

Therefore, the measure of \(\angle DBC\) is \( \boxed{18^\circ} \).