What is the total interior angle of a circle?

Answer 1

The interior angle of a circle is equal to 180 degrees. Let me sketch a "proof" for this non-intuitive result. For the purpose of simplicity and without loss of generality, let assume that a n-side polygon is regular.

Now, we can calculate the sum of the interior angles in the n-side polygon as:

(n-2)*180o (1)

where n represents the number of sides.

N order to find an interior angle in the n-side polygon we simply divide the formula (1) by n in order to get an interior angle, so:

[(n-2)*180]/n=

=(180n-360)/n

=(180n)/n-360/n

=180-360/n (2)

Now, it is easy to see that as the number of the side of the polygon increase, i.e. form a pentagon to a hexagon, the polygon becomes to look more and more like a circle. If we use equation (2) we can see that as n increases the first term stays the same 180, but the 360/n will become smaller and smaller. Now, let me imagine a is very big number "infinitely" big number then the last term will disappear and one can rewrite (2) as

180-360/n= (n becomes "infinitely big")=180.

That is the line of reasoning why the answer is 180.

Answer 2

360% by zaynah