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# ABCDE is a circular pentagon.AE is the diameter of the circle.Find the value of angle ABC + angle CDE.?

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- PopeLv 76 years agoFavorite Answer
That would be a cyclic pentagon I believe. See the sketch below. Point O is the center, and AE is a diameter.

angle ABC + angle CDE

= (1/2)(arc AEC + arc CAE)

= (1/2)[(arc AE + arc EC) + (arc CA + arc AE)]

= (1/2)[2(arc AE) + arc EC + arc CA]

= (1/2)[2(arc AE) + arc EA]

= (3/2)(arc AE)

As arc AE is a semicircle, its measure is π.

(3/2)(arc AE) = 3π/2

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- DouglasLv 56 years ago
I know what a pentagon is but I have never heard of a circular pentagon and when I googled it I did not find out.

The formula for the interior angles of a polygon are 180(n - 2) so the total angles are 540. A single angle would be 540/5 = 108. All angles of a regular pentagon are the same. That AE is the diameter of the circle is a red herring.

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