document.write( "Question 825494: The sum of three times an angle and twice its complement is 215. Find the measures of the angles. \n" ); document.write( "
Algebra.Com's Answer #497407 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 sum of three times an angle and twice its complement is 215. Find the measures of the \r\n" );
document.write( "angles.\r\n" );
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document.write( "A SOLUTION:\r\n" );
document.write( "First, we define a variable: \r\n" );
document.write( "Let m be the measure of the first angle.\r\n" );
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document.write( "We also need this definition:\r\n" );
document.write( "\"Two angles whose measures sum to 90 degrees are said to be COMPLEMENTARY.\"\r\n" );
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document.write( "Write an expression for the measure of the second angle. Since the measures of the two \r\n" );
document.write( "angles must add up to 90 degrees, the measure of the second angle is 90-a. \r\n" );
document.write( "(Note: a + 90-a = 90)\r\n" );
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document.write( "Now we translate the problem statement from English into an equation. Let's do this in steps.\r\n" );
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document.write( "\"Three times an angle\" means three times the measure of the first angle.\" We defined the \r\n" );
document.write( "measure of the angle as a. Three times a is 3a.\r\n" );
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document.write( "\"Twice the complement\" means two times the measure of the second angle. The measure of \r\n" );
document.write( "the second angle is 90-a. Two times 90-a is 2(90-a).\r\n" );
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document.write( "These two expressions added together equal 215.\r\n" );
document.write( "3a + 2(90-a) = 215.\r\n" );
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document.write( "Now we solve for a. Use the distributive property to clear the parentheses.\r\n" );
document.write( "3a + 180 - 2a = 215\r\n" );
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document.write( "Combine like terms. (3a-2a=a)\r\n" );
document.write( "a + 180 = 215\r\n" );
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document.write( "Subtract 180 from both sides to isolate the variable on the left. (180-180=0)\r\n" );
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document.write( "a + 180 - 180 = 215 - 180\r\n" );
document.write( "a = 35\r\n" );
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document.write( "In the context of this problem, a=35 means the measure of the first angle is 35 degrees. \r\n" );
document.write( "Since the the two angles are complementary, the sum of their measure is 90 degrees. Thus \r\n" );
document.write( "the measure o the second angle is 90-35=55 degrees.\r\n" );
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document.write( "Let's check these angle measures in the original problem statement:\r\n" );
document.write( "\"The sum of three times an angle and twice its complement is 215.\"\r\n" );
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document.write( "The sum of [three times 35] and [twice 55] is 215.\r\n" );
document.write( "The sum of [105] and [110] is 215.\r\n" );
document.write( "105 + 110 = 215\r\n" );
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document.write( "The measures of the two angles are 35 degrees and 55 degrees.\r\n" );
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document.write( "Hope this helps,\r\n" );
document.write( "Mrs. Figgy\r\n" );
document.write( "math.in.the.vortex@gmail.com\r\n" );
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