document.write( "Question 54048This question is from textbook
\n" ); document.write( ": The supplement of an angle is 60 degrees less than the supplement of the complement. Find the measure of the complement. \n" ); document.write( "
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Q.The supplement of an angle is 60 degrees less than the supplement of the complement. Find the measure of the complement.
\n" ); document.write( "ANS:
\n" ); document.write( "Let the angle be X .
\n" ); document.write( "Then by definition :
\n" ); document.write( "supplement of an angle is the angle which when added to the given angle completes it equal to 180 degrees.
\n" ); document.write( "complement of an angle is the angle which when added to the given angle completes 90 degrees.
\n" ); document.write( "let y be the supplement of x and m be the complement of x.
\n" ); document.write( "hence from the definition ,
\n" ); document.write( " y + x = 180
\n" ); document.write( "and m + x = 90
\n" ); document.write( "thus y = 180 - x
\n" ); document.write( "and m = 90 - x
\n" ); document.write( "according to the question , y - 60 = 180 - m
\n" ); document.write( " (180 - x) - 60 = 180 - (90 - x)
\n" ); document.write( " 180 - 60 = 90 + 2* x
\n" ); document.write( " x = 30/2 = 15 degrees
\n" ); document.write( "hence m = 90 - 15 = 85 degrees
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