Question

What is the measure of an angle that is eight times its complement? _____ degrees

Answer 1

Let's define the following variable.

x = the complement of the angle

8x = the angle

Find: the measure of the angle 8x.

Solution:

We know that the sum of the two angles that are complement to each other is 90 degrees. Hence, we can say that:

$x+8x=90$

Using the equation above, let's solve for the value of x.

$\begin{gathered} Add\text{ }similar\text{ }terms. \\ 9x=90 \\ Divide\text{ }both\text{ }sides\text{ }by\text{ }9. \\ \frac{9x}{9}=\frac{90}{9} \\ x=10 \end{gathered}$

The value of x is 10.

If x is 10, then 8x = 8 x 10 = 80.

Answer:

The measure of the angle that is eight times its complement is 80 degrees.