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)![]() ![]() 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. \n" ); document.write( "... \n" ); document.write( "Let a = an acute angle (an acute angle is < 90 degrees) \n" ); document.write( "Let b = its complement (another acute angle) \n" ); document.write( "... \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 \n" ); document.write( " |