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Question 991872: find the measures of two complementary angles if the difference in the measures of the two angle is 12
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! the two angles are x and y.
if they are complementary, then x = 90 - y
if the difference in the angles is 12, and y is the larger angle, then y = x + 12.
replace y with x + 12 in the equation of x = 90 - y to get:
x = 90 - (x + 12)
simplify to get:
x = 90 - x - 12.
combine like terms to get x = 78 - x.
add x to both sides of the equation to get 2x = 78.
divide both sides of the equation by 2 to get x = 39.
since y is 12 degrees more than x, then y must be equal to 51.
the sum of x and y is equal to 39 + 51 which is equal to 90, so the angles are comlementary.
their difference is 12 and they are complementary so the problem is solved.
your solution is that the measure of the angles is 39 and 51.
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