Question

Two angles are complementary (sum of90°). The sum of the measure of the firstangle and half the second angle is 64°.What are the measurements of the twoangles?

Answer 1

We can get two equations out of the statement

But first, we will denote the first angle as "x" and the second angle as "y".

The first equation is:

$x+y=90$

The second equation is:

$x+\frac{y}{2}=64$

We clear "y" from the second equation

$\begin{gathered} y=(64-x)\cdot2 \\ y=128-2x \end{gathered}$

Now, we replace "y" in the first equation

$\begin{gathered} x+128-2x=90 \\ x=128-90 \\ x=38 \end{gathered}$

The first angle is 38 degrees, now replace this value and we find "y"

$\begin{gathered} y=128-2(38) \\ y=128-76 \\ y=52 \end{gathered}$

The second angle is 52 degrees