Question

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? 36, 72, 18, 54

Answer 1

72

Explanation:

Step 1. Take out the least likely one. It's definitely not 18 or 36.

As it occurs to you, all you need to do is double the given angle to get 72.

Answer 2

The answer is
`m<DBC=72\°`

Explanation:

The triangle isosceles has two equal angles and two equal sides

The triangle ABC is an isosceles triangle -----> see the attached figure

`AC=AB` -----> radius of the circle

`m<DBC=m<ACB` ------> angles of the base of the isosceles triangle ABC

`m<CAB=36\°` ------> by central angle ( vertex angle of the isosceles triangle ABC)

Remember that

the sum of the internal angles of a triangle is equal to
`180\°`

so

`m<CAB+m<DBC+m<ACB=180\°`

`36\°+2m<DBC=180\°`

`m<DBC=(180\°-36\°)/2=72\°`