174k views
1 vote
In circle A shown below, Segment BD is a diameter and the measure of Arc CB is 36°

What is the measure of ∠DBC?

36°

72°

18°

54°

In circle A shown below, Segment BD is a diameter and the measure of Arc CB is 36° What-example-1
User Mikebrsv
by
8.9k points

1 Answer

2 votes

Answer: The fourth option, 54°

Explanation:

In the graph we can see that we have a triangle rectangle.

I will call each angle as the letter where it is located, the bottom angle is D, the upper left angle is C and the upper right angle is B (this last one is the angle we want to find)

This means that if the bottom angle, the angle located at D, is equal to 36°, we have that the angle located at C is equal to 90°.

And as you know, the sum of all the internal angles of a triangle must be equal to 180°, so we have:

D + C + B = 180°

90° + 36° + B = 180°

B = 180° - 90° - 36° = 54°

The correct option is the fourth one.

User Gagan Singh
by
8.2k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories