document.write( "Question 545104: The problem is: find the measure of an angle that is half as large as its complement. Help me please! \n" ); document.write( "
Algebra.Com's Answer #355457 by lmeeks54(111)\"\" \"About 
You can put this solution on YOUR website!
This problem is checking to see if you know what complementary angles are. Complementary angles are two angles that add up to a right angle (90 degrees). By the way, you don't need it for this problem, but another useful definition is supplementary angles: two angles that add up to 180 degrees.
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\n" ); document.write( "Let a = an acute angle (an acute angle is < 90 degrees)
\n" ); document.write( "Let b = its complement (another acute angle)
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\n" ); document.write( "We know by their definition that:
\n" ); document.write( "a + b = 90
\n" ); document.write( "...
\n" ); document.write( "We are given a is half as large as its complement, b:
\n" ); document.write( "b = 2a
\n" ); document.write( "...
\n" ); document.write( "Use substitution and insert the identity for b into the first equation:
\n" ); document.write( "a + b = 90
\n" ); document.write( "a + 2a = 90
\n" ); document.write( "3a = 90
\n" ); document.write( "...
\n" ); document.write( "divide both sides by 3:
\n" ); document.write( "a = 30 degrees
\n" ); document.write( "...
\n" ); document.write( "this is the answer to the problem
\n" ); document.write( "...
\n" ); document.write( "to check our work, calculate b:
\n" ); document.write( "a + b = 90
\n" ); document.write( "30 + b = 90
\n" ); document.write( "...
\n" ); document.write( "subtract 30 from both sides:
\n" ); document.write( "b = 60 degrees
\n" ); document.write( "...
\n" ); document.write( "2a = b
\n" ); document.write( "2(30) = 60
\n" ); document.write( "60 = 60 checks
\n" ); document.write( "...
\n" ); document.write( "cheers,
\n" ); document.write( "Lee
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