document.write( "Question 1210519: In a certain regular polygon, the measure of each interior angle is 2 times the measure of each exterior angle. Find the number of sides in this regular polygon. \n" ); document.write( "

Algebra.Com's Answer #853449 by MathTherapy(10753) $\"\"$ $\"About$

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document.write( "In a certain regular polygon, the measure of each interior angle is 2 times the measure of each exterior angle.\r\n" );
document.write( "Find the number of sides in this regular polygon.\r\n" );
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document.write( "The exterior angles of any polygon, sum to . Therefore, each exterior angle of any regular polygon will be ,\r\n" );
document.write( "with n being the number of sides\r\n" );
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document.write( "Since it's stated that each interior angle is TWICE each exterior angle, then each interior angle of this regular polygon =  = .\r\n" );
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document.write( "Since the 2 angles (interior and exterior) are on a straight line, they are supplementary. This gives us: \r\n" );
document.write( "                                                                                                          360 + 720 = 180n ---- Multiplying by LCD, n\r\n" );
document.write( "                                                                                                              1,080 = 180n\r\n" );
document.write( "                                                           Number of sides that this regular polygon contains, or \r\n" );
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document.write( "The regular polygon contains 6 sides, and is therefore, a regular HEXAGON!\r\n" );
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document.write( "OR\r\n" );
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document.write( "Let each exterior angle, be E\r\n" );
document.write( "Then each interior angle = 2E\r\n" );
document.write( "As these 2 angles are supplementary, we get: E + 2E = 180\r\n" );
document.write( "                                                 3E = 180\r\n" );
document.write( "Measure of each exterior angle of this regular polygon, or E = .\r\n" );
document.write( "As each exterior angle is , and the sum of the exterior angles of any polygon is , number of sides of this polygon = \r\n" );
document.write( "With 6 sides, this makes this a regular HEXAGON!

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