Question

If x is the measure of an angle, 90 - x is the measure of the complement of the angle. If the measure of the angle equals four times the measure of its complement, what is the measure of the angle?

A) 18 degrees
B) 36 degrees
C) 45 degrees
D) 72 degrees

Answer 1

The measure of an angle is four times its complement, leading to the equation x = 4(90 - x). Solving this equation results in the angle measuring 72 degrees. The correct option is D.

Step-by-step explanation:

Given that x is the measure of an angle, the measure of its complement is 90 - x. It is also given that the measure of the angle is four times the measure of its complement, which can be written as: x = 4(90 - x). To find the value of x, we solve this equation.

Expanding the equation gives us x = 360 - 4x or 5x = 360. Dividing both sides by 5 yields x = 72. Hence, the measure of the angle is 72 degrees, which corresponds to answer choice D. The correct option is D.