perplexus.info :: Geometry : Inscribed Angles in a Circumscribed Pentagon

Inscribed Angles in a Circumscribed Pentagon (Posted on 2024-05-25)

Pentagon ABCDE is circumscribed about a circle. The angles at the vertices A, C, and E of the pentagon are each 100 degrees. Find the measure of angle ACE.

No Solution Yet Submitted by Danish Ahmed Khan

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Call the center of the circle O. Angles OAE and OEA are each 100/2=50 degrees so angle AOE is 180-50-50=80 degrees.

A, C, and E are all the same distance from O so they are on a larger circle. ACE is then an inscribed angle of this new circle and so it measures 80/2=40 degrees.

Posted by Jer on 2024-05-26 11:28:30

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