SOLUTION: The measures of an angle and its complement differ by 22 degrees. Find the measures of the angles.

Question 96982: The measures of an angle and its complement differ by 22 degrees. Find the measures of the angles.
Found 2 solutions by mathslover, coyote:
Answer by mathslover(157) (Show Source): You can put this solution on YOUR website!
Let the measures of the angles be x and y
Since sum of complementary angles is 90 degrees
x + y = 90 .....(1)
also given
x - y = 22 ......(2)

Adding equations 1 and 2
we have 2x=112
or x=56
therefore y = 90 - 56 =34
angles are 56 and 34
Answer by coyote(32) (Show Source): You can put this solution on YOUR website!
Complementary angles equal 90 degrees.
x + x + 22 = 90
2x + 22 = 90
2x = 68
x = 34
So 1st angle is 34 degrees
2nd angle is 56 degrees (34 + 22)
To check: add 34 + 56 = 90
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