Question

The difference of two complementary angles is 48. Find the measures of the two angles.

Answer 1

Let x, and y represent the measures of the angles. Recall that the measure of two complementary angles adds up to 90°, therefore:

$x+y=90.$

We are given that:

$x-y=48.$

Solving the second equation for x, we get:

$x=48+y.$

Substituting the above equation in the first equation, we get:

$48+y+y=90.$

Solving for y, we get:

$\begin{gathered} 48+2y=90, \\ 2y=90-48, \\ 2y=42, \\ y=\frac{42}{2}, \\ y=21. \end{gathered}$

Now, substituting y=21 in the third equation, we get:

$x=48+y=48+21=69.$

Answer:

$69^{\circ},\text{ and 21}^{\circ}.$