Why does a triangle equal to 180 degrees?

Answer 1

A triangle has 180 degrees because it is a half of a quadrilateral and a quadrilateral can be inscribed within a circle, meaning the quadrilateral has 360 degrees as well, just like the circle. Therefore the triangle has 180. Well, why does a circle have 360 degrees? A lot of our math is based upon astronomy. The degree sign is a circle to represent the sun because it takes the earth 365 days to rotate around the sun. The Babylonians were an intelligent population and they knew this however, they disliked the number 365 for some reason. Therefore, they would count their year with 360 days and just have a party for 5 days straight, pretending that those days don't really count in the year. Therefore, we have 360 degrees in a circle, which leads to the 360 degrees of the quadrilateral, which leads to a triangle, which is half of a quadrilateral meaning it has 180 degrees. This is also where we get 60 minutes in one day, 60 seconds in a minute.

Answer 2

This was proved by Euclid, using the fact that when a transversal cuts across 2 parallel lines, the alternate interior angles are equal (and the parallel postulate). Given a triangle ABC, we use the parallel postulate to draw a line ECF parallel to AB. Then the alternate interior angles CAB and BCF are equal. Likewise, angles CBA and ACE are equal. The angles BCF, ACB, and ACE add up to the straight angle ECF. If equals be added to equals, the sums are equal, so the interior angles of the triangle add up to a straight angle, or 180 degrees.