Question 215331
If one-half of the complement of an angle plus three-fourths of the supplement of the angle equals 110.  Find the measure of the angle.


Step 1.  Let x be the angle.


Step 2.  Complementary angles means two angles add up to 90 degrees and supplementary angles means two angles add up to 180 degrees.


Step 3.  Let 90-x be the complementary angle of x and 180-x be the supplementary angle of x.


Step 4.  Let {{{(90-x)/2}}} be one half of the complementary angle.


Step 5.  Let {{{3(180-x)/4}}} be 3/4 of the supplementary angle.


Step 6.  Adding Steps 4 and 5 will be 110 degrees as given by the problem statement or in equation form we have


{{{(90-x)/2+3(180-x)/4=110}}}


Multiply by 4 to both sides of the equation toget rid of denominators


{{{4*(90-x)/2+4*3(180-x)/4=4*110}}} 



{{{2*(90-x)+3(180-x)=440}}} 


Step 7.  Solving for x yields the following steps:


*[invoke explain_simplification "2*(90-x)+3(180-x)=440" ]


Step 8.  ANSWER: The angle is 56 degrees.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J