document.write( "Question 358598: If the ratio of an angle to its supplement is 3:7 what is the ratio of the angle to its complement? Please help1!! \n" ); document.write( "

Algebra.Com's Answer #255939 by Edwin McCravy(20060) $\"\"$ $\"About$

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If the ratio of an angle to its supplement is 3:7 what is the ratio of the angle to its complement? Please help1!!
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document.write( "Let the angle have measure x°\r\n" );
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document.write( "Then the supplement of the angle = 180° - x°\r\n" );
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document.write( "Since the ratio of the angle to its supplement is 3:7, that means\r\n" );
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document.write( "           angle       3\r\n" );
document.write( "         ---------- = ---\r\n" );
document.write( "         supplement    7\r\n" );
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document.write( "              x°       3\r\n" );
document.write( "         ---------- = ---\r\n" );
document.write( "          180° - x°    7\r\n" );
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document.write( "Cross-multiply:\r\n" );
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document.write( "                7x° = 3(180° - x°)\r\n" );
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document.write( "                7x° = 540° - 3x°\r\n" );
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document.write( "               10x° = 540°\r\n" );
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document.write( "                 x° = 54°\r\n" );
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document.write( "So its complement is 90° - 54° or 36°\r\n" );
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document.write( "So to find the ratio of the angle 54° to its complement, we\r\n" );
document.write( "make the fraction:\r\n" );
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document.write( "           angle       54°\r\n" );
document.write( "         ---------- = ----\r\n" );
document.write( "         complement    36°\r\n" );
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document.write( "and reduce the fraction \r\n" );
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document.write( "            54        3 \r\n" );
document.write( "           ----  to  ---\r\n" );
document.write( "            36        2\r\n" );
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document.write( "Then change the fraction into the ratio  3:2\r\n" );
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document.write( "Edwin

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