Question 50891: Qhat are the measures of two complementary angles if the difference in the measures of the two angles is 12?
Answer by Earlsdon(6294)   (Show Source):
You can put this solution on YOUR website! Recall that if two angles are complementary, their sum is 90 degrees.
If you let the two angles be x and y, then:
x + y = 90.
In the problem description, the difference of these two angles is 12 degrees.
So you can write:
x - y = 12 By adding y to both sides, you can rewrite this as:
x = y+12 Now substitute this for x in the first equation.
(y+12) + y = 90 Simplify and solve for y.
2y+12 = 90 Subtract 12 from both sides.
2y = 78 Finally, divide both sides by 2.
y = 39 degrees, and:
x = y+12
x = 39+12
x = 51 degrees.
x+y = 90
39 + 51 = 90
90 = 90
x-y = 12
51-39 = 12
12 = 12
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