document.write( "Question 625538: The measure of an angle’s supplement is 30 degrees more than three times the measure of its complement. What is the measure of the angle? \n" ); document.write( "
Algebra.Com's Answer #393602 by math-vortex(648)\"\" \"About 
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document.write( "Hi, there-\r\n" );
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document.write( "The Problem:\r\n" );
document.write( "The measure of an angle’s supplement is 30 degrees more than three times the measure of its\r\n" );
document.write( "complement. What is the measure of the angle?\r\n" );
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document.write( "Solution:\r\n" );
document.write( "Let x be the measure of the angle.\r\n" );
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document.write( "The angle's supplement is 180-x since the measures of an angle and its supplement add up to \r\n" );
document.write( "180 degrees.\r\n" );
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document.write( "The angle's complement is 90-x since the measures of an angle and its complement add up to\r\n" );
document.write( "90 degrees.\r\n" );
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document.write( "We know that \"the measure of an angle’s supplement is 30 degrees more than three times \r\n" );
document.write( "the measure of its complement.\" Translate this statement into an algebraic equation.\r\n" );
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document.write( "[the measure of an angle's supplement] = 30 + 3 * [the measure of its complement]\r\n" );
document.write( "180-x = 30 + 3*(90-x)\r\n" );
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document.write( "Solve for x. First clear parentheses.\r\n" );
document.write( "180-x = 30 + 270 - 3x\r\n" );
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document.write( "Combine the constant terms on the right 30+270 is 300.\r\n" );
document.write( "180-x = 300 - 3x\r\n" );
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document.write( "Add 3x to both sides of the equation. On the left, -x+3x is 2x. On the right, -3x+3x=0\r\n" );
document.write( "180+2x = 300 \r\n" );
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document.write( "Subtract 180 from both sides of the equation.\r\n" );
document.write( "2x = 300-180\r\n" );
document.write( "2x=120\r\n" );
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document.write( "Divide both sides by 2.\r\n" );
document.write( "x=60.\r\n" );
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document.write( "The measure of the angle is 60 degrees.\r\n" );
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document.write( "Now check your work agains the information in the original problem.\r\n" );
document.write( "The supplement of a 60 degree angle is 120 degrees since 60+120=180.\r\n" );
document.write( "The complement of a 60 degree angle is 30 degrees since 60+30=90.\r\n" );
document.write( "A 120 degree angle is 30 more than 3 times a 30 degree angle\r\n" );
document.write( "120 is 30 more than 90. TRUE!\r\n" );
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document.write( "That's it. Please email your questions or comments. I'm happy to explain in more detail.\r\n" );
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document.write( "Ms.Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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