Two angles are complementary. One angle is fourteen times as large as the other angle. Find the measure of each angle.

Answer 1

To solve a problem like this, we can set up a system of equations.

First remember that if two angles are complementary, the sum of their angles add up to 90 degrees.

Let's give these two angles names, X and Y

Since they are complementary, we know X + Y = 90

The problem also gives us that one angle is 14 times as large as the other, let's say that Y > X.

Then we also have 14X = Y

Now we can use these two equations to solve the problem

14X = Y

X + Y = 90

X + 14X = 90

15X = 90

X = 6

14X = Y

14(6) = Y

84 = Y