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

Algebra ->  Angles -> SOLUTION: name the regular polygon in which each exterior angle is congruent with each interior angle?      Log On


   

Question 1199467: name the regular polygon in which each exterior angle is congruent with each interior angle?
Answer by ikleyn(52903) About Me  (Show Source):
You can put this solution on YOUR website!
.

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.