Q. 96 - Intermediate Algebra

Question

Translate to a system of equation and solve.

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

Step-by-Step Solution

Answer

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

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, 

$75.5+y=90$

           $y=90-75.2$

             $=17.5$