# GED Math : Supplementary Angles

## Example Questions

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### Example Question #1 : Supplementary Angles

Refer to the above diagram.

. Evaluate .

Possible Answers:

Correct answer:

Explanation:

and  form a linear pair, so they are supplementary - that is, their degree measures total , so

and  are acute angles of right triangle , so they are complementary - that is, their degree measures total , so

### Example Question #2 : Supplementary Angles

Angles A, B, and C are supplementary. The measure of angle A is . The measure of angle B is . The measure for angle C is . Find the value of .

Possible Answers:

Correct answer:

Explanation:

Since angles A, B, and C are supplementary, their measures add up to equal 180 degrees. Therefore we can set up the equation as such:

-or-

Combine like terms and solve for :

### Example Question #3 : Supplementary Angles

Angles A and B are supplementary. The measure of angle A is . The measure of Angle B is . Find the value of .

Possible Answers:

No solution

Correct answer:

Explanation:

Since angles A and B are supplementary, thier measurements add up to equal 180 degrees. Therefore we can set up our equation like such:

-or-

Combine like terms and solve for :

### Example Question #4 : Supplementary Angles

Angles A, B, and C are supplementary. The measure of angle A is . The measure of angle B is . The measure for angle C = . What are the measure for the three angles?

Possible Answers:

No solution

Correct answer:

Explanation:

Since angles A, B, and C are supplementary, their measures add up to equal 180 degrees. Therefore we can set up an equation as such:

-or-

Combine like terms and solve for x:

Plug  back into the three angle measurements:

4

### Example Question #2 : Supplementary Angles

If a set of angles are supplementary, what is the other angle if one angle is  degrees?

Possible Answers:

Correct answer:

Explanation:

Two angles that are supplementary must add up to 180 degrees.

To find the other angle, subtract 101 from 180.

The answer is:

### Example Question #5 : Supplementary Angles

What angle is supplementary to 54 degrees?

Possible Answers:

Correct answer:

Explanation:

Supplementary angles must add up to 180 degrees.

To find the other angle, we will need to subtract 54 from 180.

The answer is:

### Example Question #6 : Supplementary Angles

If  and  are supplementary angles, what must be a possible angle?

Possible Answers:

Correct answer:

Explanation:

The sum of the two angles supplement to each other will add up to 180 degrees.

Set up the equation.

Solve for .

Divide by 10 on both sides.

Substitute  for  and , and we have 36 and 144, which add up to 180.

The answer is:

### Example Question #2 : Supplementary Angles

If the angles  and  are supplementary, what is the value of ?

Possible Answers:

Correct answer:

Explanation:

Supplementary angles sum to 180 degrees.

Set up an equation to solve for .

Substitute this value to .

The answer is:

### Example Question #4 : Supplementary Angles

Suppose there are two angles.  If a given angle is , and both angles are supplementary, what must be the other angle?

Possible Answers:

Correct answer:

Explanation:

Supplementary angles add up to 180 degrees.

This means we will need to subtract the known angle quantity from 180.

Distribute the negative.

The answer is:

### Example Question #9 : Supplementary Angles

If an angle given is  radians, what is the other angle if both angles are supplementary?

Possible Answers:

Correct answer:

Explanation:

Note that supplementary angles sum up to 180 degrees or equal to  radians.

Subtract the known angle from pi.

The answer is:

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