The measure of an angle is five times the measure of a complementary angle. What is the measure of each angle?

We say two angles are complementary when they add up to a right angle, or 90°.

If we call the first angle α, we know that its complementary angle is 5 times as large, or 5α. The two angles have to add to 90°, so we can write the equation

α + 5α = 90

and solve for α. Since α + 5α = 6α, we can rewrite the equation as

6α = 90.

Dividing either side by 6, we find that α = 15, which means that 5α = 75. The measures of our two angles then are 15° and 75°.