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