Question

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

Answer 1

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.