Question

Two angles are supplementary if their sum is 180. The larger angle measures three degrees more than twice the measure of a smaller angle. If x represents the measure of the smaller angle and these two angles are supplementary, find the measure of each angle.The smaller angle measures what?The larger angle measures what?

Answer 1

We have two angles, x and y, that are supplementary.

x is the smaller angle and y is the larger angle.

If they are supplementary we can write:

`x+y=180`

The larger angle mesures 3 degrees more than twice the measure of the smaller angle.

Twice the smaller angle is 2x, so we can write:

`y=2x+3`

We can use the first equation to express y as a function of x and replace it in the second equation:

`x+y=180\Rightarrow y=180-x`

We can replace y and solve for x as:

`\begin{gathered} y=2x+3 \\ 180-x=2x+3 \\ 180-3=2x+x \\ 177=3x \\ x=(177)/(3) \\ x=59\degree \end{gathered}`

We can then calculate y as:

`y=180-x=180-59=121\degree`

Answer:

Smaller angle: x = 59°

Larger angle: y = 121°