In circle a shown below, segment bd is a diameter and the measure of arc cb is 36°: points b, c, d lie on circle a; line segment bd is the diameter of circle a; measure of arc cb is 36 degrees. what is the measure of ∠dbc?

The measure of ∠DBC is 72°.

Step-by-step explanation:

Given information: BD is a diameter, A is center of circle, Arc CB=36°.

According the angled inscribed in a semicircle theorem, the angle inscribed in a semicircle is a right angle.

According to the central angle theorem, the angle inscribed on the circle is half of its central angle.

By angle sum property, the sum of interior angles of a triangle is 180 degrees.

Therefore the measure of ∠DBC is 72°.