document.write( "Question 1183295: A polygon has two interior angles of 120 degrees each and the others are 150 degrees.Calculate a. The number of sides of the polygon b. The sum of interior angles \n" ); document.write( "

Algebra.Com's Answer #813531 by ikleyn(52839) $\"\"$ $\"About$

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document.write( "Let \"n\" be the number of sides of the polygon (the same as the number of vertices).\r\n" );
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document.write( "Two interior angles are 120 degrees each, and the other (the rest) (n-2) interior angles are 150 degrees each.\r\n" );
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document.write( "Write equation for the sum of all interior angles\r\n" );
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document.write( "    120 + 120 + (n-2)*150 = (n-2)*180.\r\n" );
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document.write( "Simplify and find \"n\"\r\n" );
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document.write( "    240 + 150n - 300 = 180n - 360\r\n" );
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document.write( "    240 + 360  - 300 = 180n - 150n\r\n" );
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document.write( "          300        = 30n\r\n" );
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document.write( "            n        = 300/30 = 10.\r\n" );
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document.write( "Thus the polygon has 10 sides and 10 vertices.\r\n" );
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document.write( "The sum of the interior angles is  (10-2)*180 = 8*180 = 1440 degrees.     ANSWER\r\n" );
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