# GED Math : Complementary Angles

## Example Questions

### Example Question #11 : Complementary Angles

If the angles  and  are complementary angles, what must be the smallest angle?

Explanation:

Complementary angles add up to 90 degrees.

Set up the equation such that both angles add up to 90.

Divide by 6 on both sides.

The smallest angle is .

Substitute the value of  into the expression.

### Example Question #12 : Complementary Angles

Suppose the angles  and  are complementary angles.  What is the value of ?

Explanation:

Complementary angles add up to 90 degrees.

Set up the equation to solve for .

Combine like-terms.

Subtract 6 from both sides.

Divide by three on both sides.

This means that .

### Example Question #13 : Complementary Angles

What angle is complement to the angle ?

Explanation:

Note that complementary angles sum up to 90 degrees.  There is no  after the fraction, which means that this value is in degrees, and not radians.

To determine the other angle, simply subtract the angle from 90 degrees.

### Example Question #14 : Complementary Angles

Which angle is complementary to the angle ?

Explanation:

Complementary angles sum up to 90 degrees.

To find the other angle, subtract 62 from the value of 90.

### Example Question #15 : Complementary Angles

The angles above are complementary.

What is the measure of the smaller angle?

Explanation:

Since the angles are complementary, you know that they must add up to a total of  degrees.  Based on our data, this means:

Simplifying, you get:

The smaller angle clearly is :

degrees

### Example Question #16 : Complementary Angles

The angles above are complementary.

What is the size of the larger angle?

Explanation:

Since the angles are complementary, you know that they must add up to a total of  degrees. Based on our data, this means:

Simplifying, you get:

It is best to compute both angles to be safe:

degrees

This means that the other is  degrees

### Example Question #17 : Complementary Angles

Complementary angles add up to how many degrees?

Explanation:

Two angles are complementary when they add up to .

### Example Question #18 : Complementary Angles

Angles and b are complementary.  If , what is the value of b?

Explanation:

Two angles are complementary when they add up to . So, to find the value of complementary angles, we will use the following formula:

Now, we know

So, we will substitute and solve for b. We get

### Example Question #19 : Complementary Angles

If two angles are complementary, and one angle is , what is the value of the other angle?

Explanation:

Two angles are complementary if they add up to . So, to find complementary angles, we will use the following formula:

Now, we know the value of one angle is , so we will substitute. We get

Now, we will solve for b. We get

Therefore, the value of the other angle is .

### Example Question #20 : Complementary Angles

What angle is complementary to ?