How to find the Exterior Angle of a Triangle in 3 Easy Steps

Get the free Exterior Angle of a Triangle worksheet and other resources for teaching & understanding solving Exterior Angle of a Triangle

Here’s how to Solve Exterior Angles of a Triangle

The Exterior Angle of a Triangle is created by the extension of one side of the triangle and the adjacent side. There are two rules for solving for an Exterior Angle of a Triangle. The first rule states that the Exterior Angle of a Triangle is equal to the sum of the two non adjacent angles. The second rule states that the Exterior Angle of a Triangle is supplementary to the adjacent angle. That means the sum of the two angles will be equal to 180 degrees. You can use either rule for finding the Exterior Angle of a Triangle by determining what information is given to you in the problem and then using the correct rule to solve.

Common Core Standard: 8.G.5

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A Short Explanation of Triangle Exterior Angle Theorem

Here’s how to find exterior angle of a triangle in a few short sentences. The Triangle Exterior Angle Theorem is made by one side of the triangle and the adjoining side. There are two things to remember when solving Triangle Exterior Angle Theorem. The primary rule that the Triangle Exterior Angle Theorem is equivalent to the total of the two non adjacent points. The second principle is that the Triangle Exterior Angle Theorem is and the angle its touching are supplementary. That implies the whole of the two points will be equivalent to 180 degrees. You can utilize either rule for finding the Exterior Angle of a Triangle by figuring out what data is given to you and using the correct rule to solve.

4 Short Steps for answering Exterior Angle of a Triangle Example Problems

The three angles in a triangle add up to 180 degrees.
The degree measure of a straight line add up to 180 degrees.
If you are given the adjacent angle you subtract the angle from 180 degrees to solve for the exterior angle of a triangle.
If you are given the two non adjacent angles you add them together to solve for the exterior angle of a triangle.

Exterior Angle of a Triangle Practice Problems Quiz

Watch the video where we complete our Exterior Angle of a Triangle Worksheet

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

Watch the free Exterior Angle of a Triangle video on YouTube here: Exterior Angle of a Triangle

Video Transcript:

This video is about exterior angles of a triangle. Here we are at our exterior angles of a triangle worksheet that you can get our on website and we’re going to do a couple practice problems from it.

We’re looking at our first problem about exterior angle theorem examples here which gives us our triangle and it also gives us our exterior angle here. You can see that we have our triangle and then we have a line that’s extended from one side of the triangle and then we’re trying to find the angle in between that line and the side of the triangle. Now in the case of this problem you have to know that all lines are all straight lines add up to 180 degrees. This right here the entire angle from one side of the line to the other is 180 degrees. When they give us a side of the triangle and they tell us that the angle of this side from here to here is a hundred and thirteen degrees that only leave.

Many degrees for this angle here so in order to find that out or in order to figure out the degree measure for this angle, all you have to do is you have to take whatever they give you in the case of this problem it’s a hundred and thirteen. We know this much of the 180 is already taken, in order to figure out what’s left over you just do 180 minus 113. We know the entire thing from here to here has to be 180 degrees from here to here is 11, you just subtract that from 180. In the case of this problem you will be left with 67 degrees. We know that X has to be equal to 67 degrees because 113 plus 67 is 180 or it’s one full line which is 180 degrees.

Number four on the triangle exterior angles worksheet gives us another triangle and a line and extends from that triangle and then it tells us to find the exterior angles of triangles that is created by that extension. Here is our angle that we are looking for now in the case of this one we don’t have an angle here and the other problem we could have just taken this angle subtracted it from 180 and it would have given us the angle that we need to figure out but in the case of this problem we do not have that.

The easiest way to do this is to take the two opposite or non adjacent angles from the exterior angle and you add them together. In the case of this triangle we have a right angle here which is of course 90 degrees and we also have 33 degrees. We’re going to take ninety degrees and we’re going to add it to 33 degrees to get 123 degrees. We know that this angle and this angle add up to 120 degrees and we know that all the angles in a triangle have to add up to 180. We could have done 180 minus 123 which gets us 57 degrees, we now know that this question mark angle is 57 degrees if you remember back to the original problem this entire thing is a straight line. It all has to add up to 180 degrees, if this amount is 57 you can do 180 minus 57 to get the remaining amount. In this case 180 minus 57 is a hundred and 23 degrees, so we know that X is 123 degrees. This is an explanation how to find angles of a triangle.

Now you may notice that this amount and this amount are the same they are equal to each other they are exactly the same, and a shortcut for solving the exterior angle of a triangle. When they give you the two non adjacent angles is to just add them together and we could have skipped these entire steps down here had we just known the rule was to add them together and that’s going to be your exterior angle measure. If you ever get a problem like this again and you have non adjacent angles to the exterior angle you just add them up and whatever they add up to is the angle measure of the exterior angle of triangle. Try all the practice problems by downloading the free triangle exterior angle worksheet above.