Question

The difference of two supplementary angles is$58$

degrees. Find the measures of the angles.

Short answer

The measures of the angles are$119$and$61$

Step-by-step solution

Step 1. Given information

The difference of two supplementary angles is$58$

degrees.

Step 2. Find angles

Let angle=$x$

then it's supplement angle =$180°-x$

Use the given condition to find $x$,

$$\begin{gathered} 180°-x-x=58° \\ 2x=180°-58° \\ 2x=122° \\ x=61° \end{gathered}$$

Supplement angle is

$$\begin{gathered} =180-61 \\ =119 \end{gathered}$$

The measures of the angles are $119°$ and $61°$.

Step 3. Check both the given conditions 

$119°+61°=180°$

This is true

$119°-61°=58°$

This is also true