document.write( "Question 622545: The measure of an angle is 20 degrees more than twice its complement. Find the measure of the smaller angle. \n" ); document.write( "

Algebra.Com's Answer #391484 by math-vortex(648) $\"\"$ $\"About$

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Hi, there--
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\n" ); document.write( "Let m be the measure of the angle.
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\n" ); document.write( "Since the sum of the measures of an angle and its complement is 90 degrees, we can write the measure of the complement as 90-m.
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\n" ); document.write( "We know that the measure of the angle is 20 degrees more than twice the complement.
\n" ); document.write( "[the measure of the angle] = [twice the measure of the complement] + [20 degrees more]
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\n" ); document.write( "In algebra we write,
\n" ); document.write( " $\"m=2%2A%2890-m%29%2B20\"$
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\n" ); document.write( "Simplify and solve for m.
\n" ); document.write( " $\"m=180-2m%2B20\"$
\n" ); document.write( " $\"m=-2m%2B200\"$
\n" ); document.write( " $\"3m=200\"$
\n" ); document.write( " $\"m=66%262%2F3\"$
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\n" ); document.write( "Since the angle measures $\"66%262%2F3\"$ degrees, its complement it $\"23%261%2F3\"$ degrees.
\n" ); document.write( "So, the smaller angle has a measure of $\"23%261%2F3\"$ degrees.
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\n" ); document.write( "It's always a good idea to check your answer against the information in the original problem.
\n" ); document.write( "Twice the complement is $\"2%2A%2823%261%2F3%29=46%262%2F3\"$ degrees. In addition, $\"66%262%2F3\"$ degrees is 20 more degrees than $\"46%262%2F3\"$ degrees.
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\n" ); document.write( "That's it! Feel free to email me if you have questions about this.
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\n" ); document.write( "Ms.Figgy
\n" ); document.write( "math.in.the.vortex@gmail.com \n" ); document.write( "

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