In a cyclic quadrilateral, opposite angles are supplementary.

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In a cyclic quadrilateral, opposite angles are supplementary.

Opposite angles in a cyclic quadrilateral sum to 180 degrees. This comes from the inscribed angle theorem: each angle measures half of the arc it intercepts. The two opposite angles intercept arcs that together make up the whole circle, whose total measure is 360 degrees. Half of 360 is 180, so those opposite angles add up to 180. This holds for any cyclic quadrilateral, not just special cases like rectangles (a rectangle also satisfies 90° + 90° = 180).

Opposite angles in a cyclic quadrilateral sum to 180 degrees. This comes from the inscribed angle theorem: each angle measures half of the arc it intercepts. The two opposite angles intercept arcs that together make up the whole circle, whose total measure is 360 degrees. Half of 360 is 180, so those opposite angles add up to 180. This holds for any cyclic quadrilateral, not just special cases like rectangles (a rectangle also satisfies 90° + 90° = 180).

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