SOLUTION: The measure of the supplement of an angle is 15 degrees less than four times the measure of the complement. Find the measure of the angle.

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Question 37726: The measure of the supplement of an angle is 15 degrees less than four times the measure of the complement. Find the measure of the angle.
Answer by jcmtnez(53) About Me  (Show Source):
You can put this solution on YOUR website!
Let call the angle X
Its complement will be 90-x
Its supplement will be 180-x
(180-x)+15 = 4(90-x)
180-x+15 = 360-4x
4x-x = 360-180-15
3x = 165
x = 55
Prove
The complement of 55 is 35
And the supplement of 55 is 125
Now we must see if the relation stated holds
125+15 = 4(35)
125+15 = 140 The measure of the supplement of an angle is 15 degrees less than four times the measure of the complement.
140 = 140
Therefore the solution of the problem is given by an angle of 55 degrees.