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### Course: High school geometry>Unit 3

Lesson 4: Theorems concerning triangle properties

# Angles in a triangle sum to 180° proof

The sum of the interior angle measures of a triangle always adds up to 180°. We can draw a line parallel to the base of any triangle through its third vertex. Then we use transversals, vertical angles, and corresponding angles to rearrange those angle measures into a straight line, proving that they must add up to 180°. Created by Sal Khan.

## Want to join the conversation?

• What is the sum of the exterior angles of a triangle?
• An easier way to explain it. A square is 360, because 90 + 90 + 90 + 90 = 360. And a square is two triangles added together. 360 divided by 2 = 180
• Even though that explanation is simple and easy to understand, there is a flaw in it. You can split a triangle into two triangles. In fact, any polygon can be viewed composed of triangles. So, following this logic, an all side symmetrical octagon is composed of 8 triangles, and the measure of all the angles in an octagon add up to 1080 degrees, so 1080/8=13.5. Meaning all the angles in a triangle add up to 13.5? And that would be false. But still, your explanation was easy to understand and I bet helped a lot of people remember this concept!:-)
• At , Sal mentions that he has "drawn an arbitrary triangle." What is an arbitrary triangle?
• Arbitary just means random. Sal means he just drew a random triangle with sides of random length.
• And how is this going to help us pay taxes as adults?
• even if they taught taxes, I'm sure everyone would still zone out
• why cant i fly
• I assume because your parents will not buy you a plane ticket.
• If the angles of a triangle add up to 180 degrees, what about quadrilaterals? Are there any rules for these shapes? ( e.g. do all of the angles in a quadrilateral add up to a certain amount of degrees?) If there is a video on Khanacademy, please give me a link.
• Consider a square. All the sides are equal, as are all the angles. A square has four 90 degree angles. 90 x 4 = 360.

• Is there a more simple way to understand this because I am not fully under standing it other than just that they add up?
• Try finding a book about it at your local library. They may have books in the Juvenile section that simplifies the concept down to what you can understand. This normally helps me when I don't get it!