May the math Gods help mii?

If a triangle is inscribed in a circle, the angles of the triangle intercept arcs that together form the circle. The total of the angles of triangles equal half a circle, or half of 360, or 180 degrees. If a quadrilateral is inscribed in a circle, the arcs intercepted by the angles overlap, so the circle is actually intercepted twice. The total of the angles of a quadrilateral is half of two circles, or half of 720, or 360 degrees. What if a pentagon is inscribed in a circle? Or any n-sided polygon? Explain how to determine the total of the angles.