Step-by-step explanation:
Inscribed angles and central angles are related to their intercepted arcs in a circle, but in different ways:
Inscribed Angle: The measure of an inscribed angle is equal to half the measure of its intercepted arc.
Central Angle: The measure of a central angle is equal to the measure of its intercepted arc.
This difference arises because inscribed angles only "see" a portion of the circle, while central angles encompass the entire intercepted arc.
In a quadrilateral inscribed in a circle, the opposite angles are supplementary (add up to 180°). This means that their intercepted arcs together form the entire circle, so their combined measure is 360°. Since an inscribed angle measures half its intercepted arc, each opposite angle must have a measure of half the circle's arc measurement, which is 180°.