The measure of an angle is 5 times as great as the measure of its complement. find the measure of the angle.

And you thought you were free of Algebra when you enrolled in Geometry didn't you? Not so fast...

[1] Let's first remember what a "complement" is. If we have angle A, then the complement of A is the angle B so that their sum is 90*. For example, the complement of a 30* angle is a 60* angle, because 30 + 60 = 90. Easy.

[2] Now, let's put Algebra in and make everyone's life miserable. Well... it's not that bad. We've got an angle A that is 5 times as great as the complement B. Let's say the complement B is x degrees, then angle A is 5 times as great or 5*x degrees.

They must add together to make 90. So:
x + 5*x = 90
6x = 90
x = 15

This is the measure of the complement B. The measure of the angle is 5 times as great or 5*x = 5*15 = 75 degrees.

We're done!