document.write( "Question 1069216: In a quadrilateral ABCD, the interior angles marked A, B, C, and D are in the ratio 6:7:8:9. Find the greatest interior angle
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Algebra.Com's Answer #684425 by ikleyn(53763) $\"\"$ $\"About$

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\n" ); document.write( "In a quadrilateral ABCD, the interior angles marked A, B, C, and D are in the ratio 6:7:8:9. Find the greatest interior angle
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document.write( "The first phrase of the condition means that there is a common measure angle \"x\" such that\r\n" );
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document.write( "A = 6x, B = 7x, C = 8x, and D = 9x.\r\n" );
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document.write( "Since the sum of interior angles of any quadrilateral is 360 degs, you have this equation\r\n" );
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document.write( "6x + 7x + 8x + 9x = 360,   or\r\n" );
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document.write( "30x = 360,   hence,   x =  = 12 degs.\r\n" );
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document.write( "Then the greatest interior angle is 9x = 9*12 = 108 degs.\r\n" );
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document.write( "Answer.  The greatest interior angle is D = 108 degs.\r\n" );
document.write( "         The greatest exterior angle is 180 - 6x = 180 - 72 = 108 degs.\r\n" );
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