if a triangle is inscribed in a circle the angles of the triangle intercept area

Question

if a triangle is inscribed in a circle the angles of the triangle intercept area 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 quaderlateral is inscribed in a circle the area intercepted by the angels overlap so the circle is actually intercepted twice the total of the angles of a quaderlateral is half of two circles or half of 720 or 380 degrees what if a pentagon is inscribed in a circle? or any nonsided polygon? explain how to determine the total of the angles

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