Question

Translate to a system of equation and solve.

The difference of two supplementary angles is$88$ degrees. Find the measures of the angles.

Short answer

The measure of the angles are$46$and$134$

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 $88$.

Therefore,$x-y=88$

Step 3. Finding the value x 

Solve for $x$:

$$\begin{gathered} x+y=180 \\ x-y=88 \end{gathered}$$

localid="1658856459175" $2x=268$

localid="1658856465563" $x=\frac{268}{2}$

localid="1658856471082" $=134$

Step 4. Finding the value y

Substitute $x=134$, in the equation

Therefore,

$y=180-134$

$=46$