Show that opposite angles of a cyclic quadrilateral are supplementry.
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The sum of the angles in each of the triangles is 180 degrees. So if we add up the labeled angle measures and the angles forming the circle around the center center, we get: 2a+2b+2c+2d+360=4\cdot 180. or a+b+c+d = 180. ... So, indeed, we see that the opposite angles in a cyclic quadrilateral are supplementary.
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