SOLUTION: If the ratio of the complement to the supplement is 4:13 then what is measurement of the original angle?

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Question 260911: If the ratio of the complement to the supplement is 4:13 then what is measurement of the original angle?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
Let the original angle be A, then its complement is (90-A) and its supplement is (180-A), so from the problem, you can write the proportion:
%2890-A%29%2F%28180-A%29+=+4%2F13 Cross-multiply.
13%2890-A%29+=+4%28180-A%29 Simplify and solve for A
1170-13A+=+720-4A Add 13A to both sides.
1170+=+720%2B9A Subtract 720 from both sides.
450+=+9A Divide both sides by 9.
50+=+A
The original angle is 50 degrees(?).
Check:
%2890-50%29%2F%28180-50%29+=+4%2F13
40%2F130+=+4%2F13
4%2F13+=+4%2F13 OK!