Why do angles add up to 360 degrees?

Answer 1

Because it is easier to use. If a right angle were to be 100 degrees when you compare it to 90, 90 has a lot more factors than 100. It's probably in the ancient days when people made it like that.

Answer 2

They don't always.

The angles inside any triangle add up to 180 degrees.

The angles inside any shape with 4 sides add up to 360 degrees.

The angles inside any shape with 5 sides add up to 540 degrees.

The angles inside any shape with 6 sides add up to 720 degrees.

If you buy a $3 surprise bag of fifty assorted angles from a military surplus store,

there's no telling what they might add up to. It could be anything.