SOLUTION: The ratio of the measures of the supplementary angle to the complementary angle of the given angle is 13:4. Then what is the measure of that angle?

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Question 825028: The ratio of the measures of the supplementary angle to the complementary angle of the given angle is 13:4. Then what is the measure of that angle?
Answer by LinnW(1048) About Me  (Show Source):
You can put this solution on YOUR website!
x = the angle
( 90 - x ) = the complement
( 180 - x ) = the supplement
13:4 = ( 180 - x ):( 90 - x )
or
%2813%2F4%29+=+%28%28+180+-+x+%29%2F%28+90+-+x+%29%29
do the cross products
4%28+180+-+x+%29=13%28+90+-+x+%29
720 - 4x = 1170 - 13x
add 13x to each side
720 + 9x = 1170
subtract 720 from each side
9x = 450
divide each side by 9
x = 50