Question

If the degree measure of an angle is 40° less than 3 times the degree measure of its supplementary angle, what is the degree measure of the angle?

Answer 1

Angle: x=?
Supplementary angle: y=180°-x

The degree measure of an angle (x) is 40° less than 3 times the degree measure of its supplementary angle (y):
x=3y-40°

Replacing y by 180°-x
x=3(180°-x)-40°
x=540°-3x-40°
x=500°-3x

Solving for x:
x+3x=500°-3x+3x
4x=500°
4x/4=500°/4
x=125°

Answer: The degree measure of the angle is 125°

Answer 2

Let the measure of the unknown angle is x °
Supplementary angles sum up to 180°. So the supplementary angle of x° will be (180 - x)°

According to the given data, measure of x is 40° less than 3 times the measure of its supplementary angle (180 - x). So we can set up the equation for this scenario as:


`x = 3(180 - x ) - 40 \\ \\ x = 540 - 3x - 40 \\ \\ x + 3x = 500 \\ \\ 4x = 500 \\ \\ x = 125`

So the degree measure of the required angle is 125°.