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Math for Kids23 chapters | 325 lessons

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Instructor:
*Allison Petrovic*

Allison has experience teaching high school and college mathematics and has a master's degree in mathematics education.

In this lesson, we will learn about the Triangle Sum Theorem. We will also look at how useful the Triangle Sum Theorem is when looking for missing angle measurements inside of a triangle.

Imagine that you are a construction worker and planning your next home to build. Working on the roof, you are trying to figure out all of the measurements. One part of the roof that you are looking at is in the shape of a **triangle**. You know it is a triangle because it is a shape with 3 sides and 3 angles. You already know that one of the angle measurements is 45 degrees. The second given angle is a right angle. Remember that a right angle is an angle that is 90 degrees. You need to figure out the third angle measurement. You are happy because you remember learning the **Triangle Sum Theorem** from math class!

The Triangle Sum Theorem states that if you add all three **interior angles**, those are the angles inside the triangle, they would add up to 180 degrees. It is easy to remember that we add the three angle measurements to get 180 degrees because of the word sum in the name of the theorem. To make it short and sweet: a + b + c = 180°

In our problem, we need to determine the third angle measurement. To find this angle measurement, all we have to do is subtract the two angle measurements that we have from 180 degrees. So, we have the following:

By using the Triangle Sum Theorem, we can say that the missing angle measurement is 45 degrees!

Let's try another example. Suppose we have a triangle with two known measurements. One of the angle measurements is 30 degrees. The second angle measurement is 60 degrees. We need to find the measurement of the third angle. Let's use the Triangle Sum Theorem to help us solve our problem! We know that the sum of all the angles inside a triangle is 180 degrees. We have two of the three angle measurements. So, all we have to do is subtract the two angle measurements that we have from 180 degrees.

180 degrees - 60 degrees - 30 degrees = 90 degrees

We can say that the third angle measurement is 90 degrees! We have a right angle!

Let's try one more example! Imagine that we have a triangle with two known measurements. The smaller of the two angles that we have is 10 degrees. The larger of the two angles that we have is 100 degrees. We need to find the measurement of the third angle. Once again, we can use the Triangle Sum Theorem! We will subtract the two angle measurements that we have from 180 degrees. Remember that the sum of all angles inside a triangle is 180 degrees.

180 degrees - 100 degrees - 10 degrees = 70 degrees

Our missing angle measurement is 70 degrees!

The **Triangle Sum Theorem** is very helpful when looking for missing angle measurements inside of a **triangle**. This theorem states that the sum of the **interior angles** of any triangle will equal 180 degrees. So, if you want to find a missing angle measurement, just subtract the angle measurements that you have from 180 degrees.

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39 in chapter 2 of the course:

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Math for Kids23 chapters | 325 lessons

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