If m∠O = 42.5°, find mDE in degrees.

Question

Use the figure below to answer the question.

A circle has center point O. There are 5 points on the circle, 4 interior line segments, and 2 highlighted arcs.

1. Point A is on the top left.
2. Point B is on the top right.
3. Point C is on the left, slightly below center.
4. Point D is on the right, slightly below center.
5. Point E is on the bottom right, below D.
6. Segments A B and B C, which lie above and left of O, form arc A C.
7. Segments O D and O E form arc D E.

If m∠O = 42.5°,

 find mDE

 in degrees.

Answer 1

The measure of a central angle (m∠O) in a circle is the same as the measure of its intercepted arc (mDE)

mDE =42.5°

Answer 2

The measure of the arc intercepted by a central angle is equal to the measure of the central angle. <0 is a central angle and DE is the arc it intercepts.