Q. 101 - Intermediate Algebra

Question

Translate to a system of equation and solve.

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

Step-by-Step Solution

Answer

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

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 $x$:

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

    $2x=268$

$x=\frac{268}{2}$

   $=134$

Step 4. Finding the value y

Substitute $x=134$, in the equation

Therefore, 

           $y=180-134$

             $=46$