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# Triangle exterior angle example

An exterior angle is formed outside a triangle by extending a side. Its measure is equal to the sum of the two non-adjacent interior angle measures, thanks to the fact that all angle measures in a triangle add up to 180 degrees. Created by Sal Khan.

## Want to join the conversation?

• Does anyone have a way to remember what supplementary and complementary mean? I keep mixing the two up when doing problems. (I mean, like a catchy phrase or something...)
• You get a COMPLEMENT when you do something RIGHT ! some complementary angles group to form a right angle (90 degreees).
• Okay uhh when he told me to pause the video i did and worked out the problem. it took me like 30 seconds but I ended up getting the same answer even though I did it a totally different way. I took two of the bottom angles 64 and 31 and I added them, which got 95. Then I subtracted that from 180 and got 85. I assumed that 85 was the whole top angle (the 50 degree angle and the unknown one). So I subtracted the known 50 degree angle from that and got 35 which was the answer. Don't know if I'm doing it wrong but do you have to do it the other way? It looks more confusing.
• the way you do it is just fine. there are just multiple ways.
• At why can't you just do this:
31+50+64+x=180
x=35
• Because connecting these two triangles would mean making a bigger triangle and the angle measurements would have to add up to 180°, this would be a way to solve this problem as well. Doing this would allow you to find the missing measurement of other part of the third angle.
• How do i remember the difference between supplementary and complementary
• Just remenber that you get compliments when you get things RIGHT! complementry angles add up to form a right angle
• I can't quite wrap my head around the idea that a triangle can have 3 angles with different degrees. Does anyone know how that is possible?
• The total of a triangles degrees is 180. With 3 intersecting sides this is possible in any number of combinations as long as the combinations of the 3 angles add up to 180 degrees.
• Do the angles of a triangle always add up to 180 degrees?
(this is prob a stupid question)
• They always add up to 180 degrees.

By the way, no question is stupid! It's just you requesting information!
• for the original triangle, couldn't you just do 180-50-64-31 and get 35?
• Yes, you can do that, but I suppose we wanted to demonstrate using triangle exterior angle here, so we don't do that
• Why is it that the Angles of a triangle add up to 180?
• An intuitive way to show this is to cut out a triangle from paper. Rip off the corners and put them together with the points of the triangle touching. If you make them all adjacent to one another, they will form 180 degrees.

To prove this, let's say we have a triangle ABC. We could create a line parallel to BC through point A. Using the angle pair relationships of parallel lines, we would find that there are two pairs of alternate interior angles that are congruent to each other. By doing this, we show that the two additional angles that were formed when we drew in the parallel line and the original interior angle A all form 180 degrees and that those two new angles are congruent to the two original interior angles at B and C.