Question

Translate to a system of equation and solve.

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

Short answer

The measures of angles are $75.5$and$17.5$

Step-by-step solution

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 complementary

Therefore$x+y=90$

Step 2. Creating the equation

The difference of two angles is $55$.

Therefore,$x-y=55$

Step 3. Finding the value x

$x+y=90$..........$\left(1\right)$

$x-y=55$...........$\left(2\right)$

Solve for $x$:

$$\begin{gathered} x+y=90 \\ x-y=55 \end{gathered}$$

$2x$ $=145$

$x=\frac{145}{2}$

$=75.5$

Step 4. Finding the value y

Substitute $x=75.5$, in the equation $x+y=90$

Therefore,

$75.5+y=90$

$y=90-75.2$

$=17.5$