Question

In circle A shown below, is a diameter and the measure of is 36°.

Answer 1

The inscribed triangle is a right triangle. The diameter of the circle served as the hypotenuse of the triangle.

Angle C is 90°
Angle D = 36°/2 = 18°

The measure of ∡DBC?

180° - 90° - 18° = 72°

Remember that interior angles of a triangle sum up to 180°.