Two angles are supplementary. One is three times the other. Find their measures.

Answer 1

Supplementary angles = 180 degrees

-If there are only two angles that make up the supplementary angle then....

Angle 1 = x

Angle 2 = 3x

and the sum of these two angles will equal 180, so now you can set up an equation and solve

x + 3x = 180

4x = 180 then divide by 4

x = 45 so angle 1 = 45 and angle 2 = 135

Answer 2

2 supplementary angles sum to 180 degrees.

Since both angles are unknown, let's define them as x and y.

Since they are supplementary, we can write the following equation:

x + y = 180.

We were also given that one is three times the other. So we can also write this equation:

x = 3y (we could also write y = 3x instead, we would get the same answers, just swapped).

using 2 equations and 2 unknowns, we can solve for x and y:

Plug x = 3y into the other equation:

(3y) + y = 180

4y = 180

y = 45 degrees

plug y back into either equation to get x:

x = 3*45 = 135 degrees