Question

In the following exercises, translate to a system of equations and solve.

The difference of two supplementary angles is 24 degrees. Find the measure of the angles.

Short answer

The measures of angles are 78 and 102 degrees.

Step-by-step solution

Step 1. Given Information   

The given data is that the difference of the two supplementary angles is 24 degrees.

Step 2. Calculation 

Let x be the first angle and y be the second angle.

Difference of the two supplementary angles is 24 degrees that is$x-y=24°--\left(1\right)$

Also, the angles are supplementary that is$x+y=180°--\left(2\right)$

Add equations (1) and (2) and solve.

$$\begin{gathered} x-y+x+y=24°+180° \\ 2x=204° \\ x=102° \end{gathered}$$

Substitute the value of x in equation (2) to find the value of y.

$$\begin{gathered} x+y=180° \\ y=180°-102° \\ y=78° \end{gathered}$$