Question

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

Answer 1

The angle measures 22.5 degrees; it is found by setting up an equation where the angle is one-third the measure of its complement and solving for the angle's measure.

Step-by-step explanation:

When we talk about complementary angles, we refer to two angles whose measures add up to 90 degrees. If we let x be the measure of the angle in question, then its complement must be 90 - x because together they must sum up to a right angle. According to the problem, the angle is one-third the measure of its complement; therefore, we can write this relationship as x = (1/3)(90 - x).

To find the measure of the angle, we solve the equation for x:

• 3x = 90 - x
• 4x = 90
• x = 22.5 degrees

Therefore, the angle measures 22.5 degrees.

Answer 2

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