SOLUTION: If one-half of the complement of an angle plus three-fourths of the summplement of the angle equals 110 degrees, find the measure of the angle.

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Question 83462This question is from textbook
: If one-half of the complement of an angle plus three-fourths of the summplement of the angle equals 110 degrees, find the measure of the angle. This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the measure of the required angle be x.
One half the complement of x is %281%2F2%29%2890-x%29 and three fourths of the supplement of x is%283%2F4%29%28180-x%29 The sum of thease is 110 degrees, so...
%281%2F2%29%2890-x%29%2B%283%2F4%29%28180-x%29+=+110 Simplify and solve for x. Multiply through by 4 to clear the fractions.
2%2890-x%29%2B3%28180-x%29+=+4%28110%29 Expand.
180-2x%2B540-3x+=+440 Combine like-terms.
720-5x+=+440 Subtract 720 from both sides.
-5x+=+-280 Divide both sides by -5.
x+=+56degrees.
Check:
= 17%2B93+=+110 OK!