Question

Translate to a system of equation and solve.

The difference of two supplementary angles is$8$ degrees. Find the measures of the angles.

Short answer

The measure of the angle are$86$and$94$

Step-by-step solution

Step 1. Given information

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 difference of two angles is $8$.

Therefore,$x-y=8$

Step 3. Finding the value x

$x+y=180$..........

$x-y=8$...........

Solve for $x$:

$$\begin{gathered} x+y=180 \\ x-y=8 \end{gathered}$$

$2x=172$

$x=\frac{172}{2}$

$=86$

Step 4. Finding the value y

Substitute $x=86$, in the equation$x+y=180$

Therefore,

$x+y=180$

$y=180-86$

$=94$