>>13598011Here's the demonstration. As you can see from pic related the sum of the inner angles of a polygon can be obtained by calculating (n-2)*180 with n being the number of sides of the polygon. A circle is nothing but a polygon with infinite sides so the sum of the inner angles of a circle is:
lim (n-2)*180
n->infinity
Now in the case of regular polygons (which the circle is) the angles of the polygon are all identical and therefore can be calculated by dividing the sum of the angles by the number of angles like this ((n-2)*180)/n. We can use this property in the circle to calculate 2*alpha:
2*alpha= ((n-2)*180)/n
Therefore:
alpha=((n-2)*180)/2n
Now all we need to do is plug in the value of n which in this case tends towards infinity:
lim ((n-2)*180)/2n
n->infinity
Now just plug that into a limit calculator and you'll find the answer is 90.
