Q. 100 - Intermediate Algebra

Question

Translate to a system of equation and solve.

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

Step-by-Step Solution

Answer

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

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, 

$x+y=180$

           $y=180-86$

             $=94$