SOLUTION: The sum of the measures of a complement and a supplement of an angle is 160. Find the measure of the angle.

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Question 1126292: The sum of the measures of a complement and a supplement of an angle is 160. Find the measure of the angle.
Answer by MathLover1(20849) About Me  (Show Source):
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Supplementary angles are two angles that have a sum of 180°.
Complementary angles are two angles that have a sum of 90°.
i angle is alpha, its supplement is 180-+alpha, and its complement is 90-+alpha
if the sum of the measures of a complement and a supplement of an angle is 160, we have
%28180-+alpha%29%2B%2890-+alpha%29=160...solve or alpha
180-+alpha%2B90-+alpha=160
270-+2alpha=160
270-160+=+2alpha
110+=+2alpha
alpha=110+%2F2
alpha=55°
check:
if alpha=55, its supplement is 180-+alpha=180-55=125
if alpha=55, its complement is 90-+alpha=90-55=35
125%2B35=160
160=160