Question 1199467
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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:



<pre>
    (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.
</pre>


Solved, with full explanations.