Question

An angle measures 24.6° more than the measure of its complementary angle. What is the measure of each angle? _and_

Answer 1

You have two angles, let's call them ∠1 and ∠2 of unknown measure, one of them measures 24.6º more than the other and both angles are complementary.

Let "xº" be the measure of ∠1, then ∠2 will beasure (x+24.6)º

∠1 and ∠2 are complementar, this means that together they add up to 90º

`\angle1+\angle2=90º`

Replace the expression with the angles measures

`x+(x+24.6)=90`

And solve for x

`\begin{gathered} 2x+24.6=90 \\ 2x=90-24.6 \\ 2x=63.6 \\ (2x)/(2)=(65.4)/(2) \\ x=32.7 \end{gathered}`

The angles measure:

∠1=32.7º

∠2=32.7+24.6=57.3º