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

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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. \\ (9x)/(9)=(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.

User Cosmina Palade
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