Why are opposite angles of an inscribed quadrilateral supplementary?

An inscribed quadrilateral is a four-sided figure inside a circle that has each of its vertices (corners) on the circle. Each vertex is an angle whose legs intersect the circle at the adjacent vertices.The measurement in degrees of an angle like this is equal to one half the measurement in degrees of the arc of the circle that is included between the legs of the angle. A pair of opposite vertices will have legs that intersect the circle at the remaining two vertices. Between the two of them, they will include arcs that make up the entire 360 degrees of the circle, Therefore, the sum of these two angles in degrees, no matter what size one of them might be, will always be 180 degrees (half of 360 degrees). Two angles that add up to 180 degrees are called supplementary.

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