SOLUTION: if an angle is 30 degree more than one half of its complement, find the measure of the angle?

Question 1035707: if an angle is 30 degree more than one half of its complement, find the measure of the angle?
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x is the angle.
90 - x is its complement.
if the angle is 30 degree more than one half of its complement, then .....
x = 1/2 * (90 - x) + 30
simplify this to get x = 45 - 1/2 * x + 30
simplify further to get x = 75 - 1/2 * x
add 1/2 * x to both sides of this equation to get x + 1/2 * x = 75
simplify to get 1.5 * x = 75.
solve for x to get x = 75 / 1.5 = 50.

the angle is 50 degrees.
its complement is 90 - 50 = 40 degrees.
the angle is 30 degrees more than half its complement.
half its complement is 20.
20 + 30 = 50
solution looks good.

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