Question

An angle is equal to one-third of its complement. Find the angle's measure.

Answer 1

Let $x^\circ$ be the measure of the angle in question. Its complement has measure $(90-x)^\circ$. We're told that this angle is congruent to 1/3 of its complement, so that

$x^\circ=\dfrac{(90-x)^\circ}3\implies3x^\circ=(90-x)^\circ\implies4x^\circ=90^\circ\implies x=22.5^\circ$