Question

The measure of the complement of an angle is 15 degrees smaller than the measure of the angle. What is the measure of each angle?

Answer 1

Let x be the measure of the angle and y be the measure of its complement.

Given that the complement angle is 15 degrees less than x, that is, y = x - 15.

Use the relation that sum of an angle and its complement equals 90 degrees. So,

`x+y=90`

Substitute x-15 for y into the equation.

`\begin{gathered} x+x-15^(\circ)=90^(\circ) \\ 2x-15^(\circ)=90^(\circ) \\ 2x=105^(\circ) \\ x=(105^(\circ))/(2) \\ =52.5^(\circ) \end{gathered}`

The measure of the angle is 52.5 degrees and of its complement is 37.5 degrees.