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=(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).`