What is the relationship between opposite angles in a cyclic quadrilateral?

In a cyclic quadrilateral, which is defined as a four-sided figure where all corners or vertices lie on a single circle, the relationship between opposite angles is that their sum is always 180°. This means if you take one angle, its opposite angle will complement it to equal 180° when combined.

This property arises from the concept that the angles subtended by the same arc at the circumference of the circle are equal. Therefore, if you take two opposite angles, they subtend arcs that together complete the full circle, resulting in their sum being half the total degrees of a circle (360°), which leads to the conclusion that they sum to 180°.

Understanding this relationship is crucial in solving various problems involving cyclic quadrilaterals, as it allows for the calculation of unknown angles and reinforces the principles of angles in circles. This property of opposite angles does not imply that they are equal or complementary in any other specific manner, but rather that their combined measure is 180°, which is distinct and significant in geometry.