Question

Find the measure of the arc or angle indicated. Show your work.

Answer 1

In any circle, the measure of an inscribed angle is half the measure of its subtended arc, also the measure of the inscribed angle subtended by the diameter of the circle is 90 degrees

From the given figure

Since CE is the diameter of the circle

Since < CDE subtended by the diameter CE

The m < CDE = 90 degrees

Since < ECD is an inscribed angle subtended by the arc ED

m < ECD = 1/2 m arc ED

Since the measure of arc ED is 76 degrees

m < ECD = 1/2 x 76 = 38 degrees

In triangle CDE

m < CDE = 90 degrees

m < ECD = 38 degrees

Then

m < CED = 180 - 90 - 38

m < CED = 52 degrees