Question

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

The difference of two complementary angles is 55 degrees. Find the measures of the angles.

Short answer

The measures of angles are $17.5and72.5$degrees.

Step-by-step solution

Step 1. Given Information  

The given data is that the difference of the two complementary angles is 55 degrees.

Step 2. Calculation  

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

Difference of the two complementary angles is 88 degrees that is $x-y=55°--\left(1\right)$

Also, the angles are complementary that is $x+y=90°--\left(2\right)$

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

$$\begin{gathered} x-y+x+y=55°+90° \\ 2x=145° \\ x=72.5° \end{gathered}$$

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

$$\begin{gathered} x+y=90° \\ y=90°-72.5° \\ y=17.5° \end{gathered}$$