The measure of the supplement of an angle is four times that of its complement. Find the angle.

Question

The measure of the supplement of an angle is four times that of its complement. Find the angle.

Answer 1

Hello, thank you for taking the time to post your question!

The complement of an angle is 90 – x and the supplement of an angle is 180 – x … since it’s saying that the measure of the supplement is four times that of its complement we can set up the algebraic equation

Supplement = 4 * Complement

(180 – x) = 4(90 – x)

From there then it’s just a matter of solving for the value of “x” algebraically

180 – x = 360 – 4x

3x = 180

x = 60

so the angle that it’s after here is 60 degrees

I hope that helps get you moving in a better direction on this type of question! Feel free to reach out if you have any additional questions beyond that :)

Answer 2

Let x = original angle

 

Let y = the angle's complement

 

Let 4y = the angle's supplement 

 

Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees.

 

x + y = 90

 

x + 4y = 180

 

Subtract the two equations: 

 

-3y = -90

 

y = 30

 

x = 60 degrees

 

The original angle is 60 degrees.