Why do the angles in a triangle add up to 180°??

My goal on this channel is to make short, easy-to-understand videos exploring topics that we may have just memorized to be true but never actually proved. Have you proved before why all the angles in a triangle always add up to 180 degrees? Can you think of any other ways to prove this?

Whether you're already a lover of mathematics, or you're someone who thinks math is the farthest thing from "cool", I hope you stick around, learn something new, or just find something to appreciate about the mathematics all around us.

Tell me what other proofs or videos you'd like to see on my channel!

[talismanskulls]

Or you can take one angle and tilt it 34.86º and connect the the ends by two 90º angles which totals 214.86º. You just draw one vertical line for the top end and down to meet the horizontal one drawn from the other end so they connect at the bottom as an L shape more or less. Thus you still have achieved an irregular triangle that does not break any rules but still is not a total of only 180º. It all is relative to the length of the lines so therefore the assumption of no triangle can add up to anything but 180º is false.

[fellajobbie]

Great video thanks I was always wondering why this was true 👍

[plenin]

In the case of spherical triangle the sum of three angles is greater than 180 degree and to be more specific the sum equals to 540 degrees. Your explanation is true only for plane triangle.

[angeldude]

Of course this only works if the two lines really _are_ parallel, and in euclidean space, they are. In non-euclidean space, their isn't necessarily a unique line parallel line to the base. Accordingly, the interior angles don't necessarily add up to 180 degrees, and can be greater or less than 180 degrees depending on the exact geometry.
This is pretty easy to show by drawing an equilateral triangle on a globe with 3 right angles; two on the equator, and one at a pole.