In the circle shown below, segment BD is a diameter and the measure of arc CB is 36°. What is the measure of ∠DBC?

Solution:

Give, BD is the diameter

Measure of arc CB is 36°.

The triangle ABC is an isosceles triangle.

In an isosceles triangle, two sides and two angles are equal.

From the figure, 

AC = AB → radius of the circle

∠DBC = ∠ACB → angles of the base of the isosceles triangle

∠CAB = 36° → vertex angle of the isosceles triangle

We know, sum of interior angles = 180°

So, ∠CAB + ∠DBC +∠ACB = 180°

Since, ∠ACB = ∠DBC

36° + 2∠DBC = 180°

2∠DBC = 180°- 36°

∠DBC = 154°/2

∠DBC = 72°

Therefore, the measure of ∠DBC is 72°.

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In the circle shown below, segment BD is a diameter and the measure of arc CB is 36°. What is the measure of ∠DBC?

Summary:

In the circle shown, segment BD is a diameter and the measure of arc CB is 36°. The measure of ∠DBC is 72°.