Question

Translate to a system of equation and solve.

Two angles are supplementary. The measure of the larger angle is four more than three times the measure of the smaller angle. Find the measures of the angles.

Short answer

The measure of the angle are $136$ and $44$.

Step-by-step solution

Step 1. Given information

$x$Suppose x represents the measure of the first angle.

and similarly, $y$represents the measure of the second angle

Now, both the angles are supplementary

Therefore,

$x+y=180$

Step 2. Creating the equation  

The larger angle is four more than three times the smaller angle

Therefore,$x=4+3y$

Step 3. Finding the value y

Solve for $x$:

$$\begin{gathered} x+y=180 \\ 4+3y+y=180 \\ 4+4y=180 \\ 4y=180-4 \\ 4y=176 \\ y=\frac{176}{4} \\ =44 \end{gathered}$$

Step 4. Finding the value x 

Substitute $y=44$into $x=4+3y$

$$\begin{gathered} x=4+3y \\ x=4+3\left(44\right) \\ =4+132 \\ =136 \end{gathered}$$