Why do squares and circles both have 360 degrees?

[mrigakshigoel]

So if we assume that every angle in the square is 20 degrees instead of 90. Now the circle and square will have total 80 degrees and same calculus follows for other geometry. But why did we choose a right angle is 90, straight line is 180 and circle 360.

[ColinSemple]

While I know we all say that a circle is 360 degrees, it actually isn't true. By drawing two lines that intersect at 90 degrees at the dead centre you do get an inverted square. Now at each point where the straight line touches the perimetre draw a straight line to the other line where it intersects the perimetre. You now have four triangles inside the square and the circle. The angles at the perimetre must be 45 degrees to match the 180 degrees of a triangle. But clearly there is space outside of the triangle where the circle is. In fact, as you move along the hypotenuse you can see the respective angle increasing beyond 45 degrees. This demonstrates that the angle that is exterior to the triangle must be more than 45 degrees. That's the problem with using just the interior angle alone. But for simplicity we use 360 degrees for a circle since infinity would be impractical.

[masmas]

They are inversions of each other. This is our universe.

[AvrgJoe]

I’m also curious about the (n-2)=180. Why is that? Math is so amazing! It’s the language of the universe. There’s no BS interpretation. And the secrets it reveals are amazing.

[adriennevincent]

Someone who already knows why a square is 360 degrees could follow this, I presume, but for someone who wants to learn, meh! Explain why you subtract 2 from 4, for example.

[StarWarsMasters]

A square is a circle guys it has been proven XD