document.write( "Question 260911: If the ratio of the complement to the supplement is 4:13 then what is measurement of the original angle? \n" ); document.write( "

Algebra.Com's Answer #192215 by Earlsdon(6294) $\"\"$ $\"About$

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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:
\n" ); document.write( " $\"%2890-A%29%2F%28180-A%29+=+4%2F13\"$ Cross-multiply.
\n" ); document.write( " $\"13%2890-A%29+=+4%28180-A%29\"$ Simplify and solve for A
\n" ); document.write( " $\"1170-13A+=+720-4A\"$ Add 13A to both sides.
\n" ); document.write( " $\"1170+=+720%2B9A\"$ Subtract 720 from both sides.
\n" ); document.write( " $\"450+=+9A\"$ Divide both sides by 9.
\n" ); document.write( " $\"50+=+A\"$
\n" ); document.write( "The original angle is 50 degrees(?).
\n" ); document.write( "Check:
\n" ); document.write( " $\"%2890-50%29%2F%28180-50%29+=+4%2F13\"$
\n" ); document.write( " $\"40%2F130+=+4%2F13\"$
\n" ); document.write( " $\"4%2F13+=+4%2F13\"$ OK!
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