SOLUTION: name the regular polygon in which each exterior angle is congruent with each interior angle?

Question 1199467: name the regular polygon in which each exterior angle is congruent with each interior angle?
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
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This regular polygon is a square.

Each interior angle of a square is 90 degrees.

The same measure has every exterior angle of a square.

The proof is in three steps:

    (a)  The sum of interior and exterior angles is 180 degrees

             I + E = 180  degrees


    (b)  The angles are congruent, hence, they have equal angular measures

             I = E.


    (c)  We substitute I instead of E into equation (1), based on (2), and we get then

             I + I = 180 degrees,  2*I = 180 degrees,  I = 180/2 = 90 degrees.

         which is the measure of an interior angle of a square.

Solved, with full explanations.

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