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# What you need to know about Triangle Sum Theorem

Get the free Triangle Sum Theorem worksheet and other resources for teaching & understanding Triangle Sum Theorem

## Here’s how to Solve Triangle Sum Theorem

Triangle Angle Sum Theorem is mathematical proof about the interior angles of a triangle. The Triangle Angle Sum states that all the angles inside of a triangle must add up to 180 degrees. This means that you can use the Triangle Angle Sum to find a missing interior angle of a triangle by adding the two angles that you know together and then subtracting the sum from 180 degrees. Continue below to try some Triangle Sum Theorem Practice Problems or click the download links on the right to download a free Triangle Angle Sum Theorem Worksheet.

Common Core Standard: 8.G.5

## What do the angles of a triangle add up to?: A Short Answer

Triangle Angle Sum Theorem is the sum of the inside angles of a triangle. The Triangle Angle Sum expresses that every angle within a triangle must add up to 180 degrees. This implies you can utilize the Triangle Angle Sum to locate a missing inside edge of a triangle by adding the two angles that you know together and after that subtracting the amount from 180 degrees.

## 3 Simple Steps for finding the Sum of Interior Angles of a Triangle

1. Add the two angles that you know together.
2. Take the sum of those two angles and subtract it from 180.
3. The resulting amount is the missing angle.

## What is Triangle Sum Theorem? Try the Practice Problem

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Triangle Sum Theorem Quiz

Click Start to begin the practice quiz!

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Find x for the missing angle measure of the following triangle:

Angle 1: 85 degrees

Angle 2: 20 degrees

Angle 3: x degrees

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Find x for the missing angle measure of the following triangle:

Angle 1: 45 degrees

Angle 2: 60 degrees

Angle 3: x degrees

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Find x for the missing angle measure of the following triangle:

Angle 1: 23 degrees

Angle 2: 132 degrees

Angle 3: x degrees

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Find x for the missing angle measure of the following triangle:

Angle 1: x degrees

Angle 2: 57 degrees

Angle 3: 117 degrees

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Find x for the missing angle measure of the following triangle:

Angle 1: 67 degrees

Angle 2: x degrees

Angle 3: 98 degrees

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## Watch and follow the video where we complete our Triangle Sum Worksheet

Watch our free video on how to solve Triangle Angle Sum Theorem. This video shows how to solve problems that are on our free Triangle Angle Sum worksheet that you can get by submitting your email above.

Watch the free Sum of Angles in a Triangle video on YouTube here: Triangle Sum Theorem

Video Transcript:

This video is about the triangle sum theorem. In order to show you some examples about the triangle sum theorem we’re going to use our worksheet that you can get on our website mathcation.com.

The first thing we need to know about the triangle sum theorem is the rule that all the angles in a triangle have to add up to 180 degrees. Angle 1 plus angle 2 plus angle 3 will always add up to 180 degrees. In the case of our first problem we are given 34 degrees 97 degrees and then we’re missing this angle here. We have to find this missing angle here. The easiest way to do this is to add up these two. 34 which we’re going to say is angle 1 plus angle 2 which is 97 plus measure of angle 3, which we don’t know, is equal to 180 degrees. Now we’re going to add these two together 34 plus 97 is 131 and then we don’t know the measure of angle 3 and it’s 180 degrees. Then the last step is to subtract 180 minus 131 to get our answer of 49 degrees  the measure of angle 3 will be equal to 49 degrees.

Moving onto number 2 we’re given a new triangle and we’re given 24 degrees here and then we’re given a right angle here. All right angles are equal to 90 degrees. A shortcut to do this instead of doing the way we did in problem 1 would be to add these two together and then subtract it from 180 degrees. The quickest way to do this would be 90 plus 24 which is equal to 114 degrees and then you just do 180 minus 114 because they have to add up to 180. 180 minus 114 if 66. This angle here has to be 66 degrees because all three angles must add up to 180. 66 plus 24 plus 90 equals 180. We know that’s our answer.

You can find other triangle sum theorem worksheet answers when you download the free triangle angle sum theorem worksheet. The free download includes a practice worksheet as well as the triangle sum theorem answer key.

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