document.write( "Question 1199467: name the regular polygon in which each exterior angle is congruent with each interior angle? \n" ); document.write( "

Algebra.Com's Answer #833353 by ikleyn(52803) $\"\"$ $\"About$

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\n" ); document.write( "\n" ); document.write( "This regular polygon is a square.\r
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\n" ); document.write( "\n" ); document.write( "Each interior angle of a square is 90 degrees. \r
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\n" ); document.write( "\n" ); document.write( "The same measure has every exterior angle of a square.\r
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\n" ); document.write( "\n" ); document.write( "The proof is in three steps:\r
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document.write( "    (a)  The sum of interior and exterior angles is 180 degrees\r\n" );
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document.write( "             I + E = 180  degrees\r\n" );
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document.write( "    (b)  The angles are congruent, hence, they have equal angular measures\r\n" );
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document.write( "             I = E.\r\n" );
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document.write( "    (c)  We substitute I instead of E into equation (1), based on (2), and we get then\r\n" );
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document.write( "             I + I = 180 degrees,  2*I = 180 degrees,  I = 180/2 = 90 degrees.\r\n" );
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document.write( "         which is the measure of an interior angle of a square.\r\n" );
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\n" ); document.write( "\n" ); document.write( "Solved, with full explanations.\r
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