SOLUTION: The sum of the measures of two complementary angles exceeds the difference of the measures of their supplements by 32 degrees. Find the measure of each angle.

Question 1123535: The sum of the measures of two complementary angles exceeds the difference of the measures of their supplements by 32 degrees. Find the measure of each angle.
Found 2 solutions by greenestamps, rothauserc:
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

The angles are complementary, so their measures are x and 90-x.

The supplements are 180-x and 180-(90-x) = 90+x.

The difference between the two supplements is (180-x) - (90+x) = 90-2x.

The problem says the sum of the two angles (90) exceeds the difference between the supplements by 32 degrees:

90 = (90-2x)+32

Easily solved from there....
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
1) x + y = 90
:
2) x + s1 = 180
:
3) y + s2 = 180
:
90 = s1 -s2 +32
:
4) s1 - s2 = 90 - 32 = 58
:
solve equation 2 and equation 3 for s1 and s2
:
s1 = 180 - x
:
s2 = 180 - y
:
substitute for s1 and s2 in equation 4
:
(180 - x) - (180 - y) = 58
:
5) y - x = 58
:
use equations 1 and 5, we have two equations in two unknowns
:
solve equation 1 for y
:
y = 90 - x
:
substitute for y in equation 5
:
90 - x - x = 58
:
-2x = -32
:
x = 16
:
y = 90 - 16 = 74
:
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x = 16 degrees and y = 74 degrees
:
s1 = 180 - 16 = 164 degrees
:
s2 = 180 - 74 = 106 degrees
:
x + y = 90 degrees
:
s1 - s2 = 164 - 106 = 58 degrees
:
Note 58 + 32 = 90 degrees
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