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

$\begin{gathered} 2x+24.6=90 \\ 2x=90-24.6 \\ 2x=63.6 \\ \frac{2x}{2}=\frac{65.4}{2} \\ x=32.7 \end{gathered}$

The angles measure:

∠1=32.7º

∠2=32.7+24.6=57.3º