Question

"1 of 2 complementary angles added to ½ the other yields 62°.Find the measure of the two angles"

Answer 1

Task. One of two complementary angles added to $\frac{1}{2}$ the other yields $62{}^{\circ}$. Find the measure of the two angles.

Solution. Let $x$ and $y$ be these angles. Since they are complementary, we have that

$x+y=90,$

and so

$x=90-y.$

On the other hand, by assumption, $x$ added to $\frac{1}{2}$ of $y$ yields $62{}^{\circ}$, so

$x+y/2=62.$

Substituting $x=90-y$ we obtain

$90-y+y/2=62,$

$90-y/2=62,$

$y/2=90-62=28,$

$y=2*28=56{}^{\circ},$

whence

$x=90-56=34{}^{\circ}.$

Answer. $34{}^{\circ},~{}56{}^{\circ}.$