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Find the measure of arc ED

Find the measure of arc ED-example-1
User Rbacarin
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1 Answer

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Answer:

38°

Explanation:

You want the measure of arc ED in the diagram shown.

Complementary angles

Call the center of the circle point O. Angle AOB is complementary to the angle marked 52°. That means the measure of angle AOB is ...

∠AOB = 90° -52° = 38°

Vertical angles

Angle EOD is a vertical angle with respect to angle AOB, so is congruent to it. This means angle EOD is also 38°.

The measure of arc ED is the same as the measure of central angle EOD.

Arc ED is 38°.

User Niels Billen
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