A polygon is inscribed in a circle if its vertices are points on circle and the sides of it are chords of the circle. Equivalently, circle is said to be constrained about the polygon. A polygon is circumscribed about a circle if all the sides of polygon are segments tangent to the circle; and also the circle is said to be inscribed in the polygon. There are several types of polygons ... each with sides and angles. When we talk about the angles of the polygon, we mean the interior angles. A polygon has as various interior angles as sides. An equilateral triangle has three angles each of 60 degree angles. The sum of the angles of triangle is 180 degrees. The sum of the 4 interior angles of a square is 360 degrees, which is the same for any quadrilateral. The sum of interior angles increases by 180 degrees for every additional side ... heptagon, hexagon, pentagon, octagon ... as polygons have more sides, the interior angles become larger and there are more of them, so the sum of the interior angles increases. There are other angles related to polygons which are exterior angles. An exterior angle is formed by extending 1 side at each vertex. As the number of side's increases, exterior angles become smaller.

 Central Angle Postulate
 In a circle, degree measure of a central angle is equal to the degree measure of the intercepted arc of it. When 2 chords intersect "inside" a circle, 4 angles are formed. If 2 chords intersect in the interior of a circle, then the measure of each angle is half of the measures of the arcs intercepted by angle and its vertical angle.

If a tangent and a chord intersect at a point on a circle, then measure of each angle formed is half the measure of its intercepted arc.

If two chords intersect in the interior of a circle, then measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

If a tangent and a secant, 2 tangents, or two secants intersect in the exterior of a circle, then measure of the angle formed is half the difference of the measures of the intercepted arcs.

If a tangent and a secant, 2 tangents, or 2 secants intersect in the exterior of a circle, then measure of the angle formed is half the difference of measures of intercepted arcs. If a tangent and chord intersect at a point on a circle, then the measure of each angle formed is half the measure of its intercepted  arc.

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