Question

The measure of the angles supplement is 30 degrees more than five times that of its complement. Find the measure of the angle described.

Answer 1

Supplement
Let the original angle = x
The supplement is 180 - x

The complement
The compliment = 90 - x
5 times the compliment = 5*(90 - x)
Thirty degrees more = 5*(90 - x) + 30

Equation
So the supplement = 5*(90 - x) + 30
180 - x = 5(90 - x) + 30 Remove the brackets

Solution
180 - x = 450 - 5x + 30 Combine like terms on the right.
180 - x = 480 - 5x Add 5x to both sides
180 - x + 5x = 480
180 + 4x = 480 Subtract 180
4x = 480 - 180
4x = 300 Divide by 4
x = 300/4
x = 75

Check
The supplement = 180 - 75 = 105
The complement = 90 - 75 = 15

5 Times the complement = 15*5 = 75
Plus 30 = 75 + 30 = 105 They do check.

Answer
The original angle = 75