# GED Math : Supplementary Angles

## Example Questions

### Example Question #11 : Supplementary Angles

Which angle must be supplementary to the angle ?

Explanation:

Supplementary angles add up to 180 degrees.

Subtract  from 180 degrees.  Do not add this value with 180!

### Example Question #12 : Supplementary Angles

The angles above are supplementary.

What is the angle measure of the smaller angle above?

Explanation:

Since the two angles are supplementary, you know that they must add up to  degrees.  Therefore, you can take their values and create the following simple equation:

Next, solve for :

Now, be careful!  Substitute back in to find your angle measures:

### Example Question #13 : Supplementary Angles

The angles above are supplementary.

What is the smaller of the two angle measures?

Explanation:

Since the two angles are supplementary, you know that they must add up to  degrees.  Therefore, you can take their values and create the following simple equation:

Simplify to find :

Then, put  back in to find the smaller measure:

Thus, the smaller angle is  degrees.

### Example Question #14 : Supplementary Angles

The angles above are supplementary.

What is the sum of the two smaller angles in those above?

Explanation:

To begin, note that the angles are supplementary.  This means that they must add up to  degrees.  Based on your data, this means:

Simplifying, you get:

Since  is  degrees, you know that your three angles are:

Therefore, the sum of your two smallest angles is  degrees.

### Example Question #15 : Supplementary Angles

There are three angles that, altogether, are supplementary. The second angle is 10 degrees larger than the first, while the third is 10 larger than the second. What is the size of the middle-sized angle?

Cannot be computed from the information provided

Explanation:

Since all three angles are supplementary, you know that they must add up to  degrees. However, you need to manage some of the other details. Imagine that the first one is  degrees. The second must be  degrees. This means that the third is  or  degrees. Therefore, you could draw the following:

Based on this data, you know:

Simplifying, you get:

The middle angle is  or  degrees

### Example Question #16 : Supplementary Angles

Angles x and y are supplementary.  If , what is the value of x?

Explanation:

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

Now, we know . So, we can substitute and solve for x. We get

### Example Question #17 : Supplementary Angles

Suppose a pair of angles are supplementary.  What is the other angle if one angle is ?

Explanation:

Supplementary angles add up to 180 degrees.

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

Combine like-terms.

### Example Question #18 : Supplementary Angles

Angles x and y are supplementary.  If , find x.

Explanation:

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

Now, we know  So, we will substitute and solve for x. We get

### Example Question #19 : Supplementary Angles

If two angles are supplementary, where one given angle measurement is  degrees, and the other angle is  degrees,what must be the value of ?

Explanation:

Set up an equation such that both angles will add up to 180 degrees, since these are supplementary angles.

Combine like-terms.

Subtract fifty from both sides.

Divide by 100 on both sides.

### Example Question #20 : Supplementary Angles

Figure NOT drawn to scale.

Refer to the above figure. Evaluate .