Use the theorems that you that you have learned about inscribed angles and intercepted arcs to explain why inscribed quadrilaterals have opposite angles that are supplementary. Answer in 5-6 lines.
See:
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To understand why opposite angles in an inscribed quadrilateral are supplementary, we can use the theorem that states an inscribed angle is half the measure of its intercepted arc.
Considering an inscribed quadrilateral, each angle of the quadrilateral is an inscribed angle with its intercepted arc. Let's label these angles as A, B, C, and D.
Using the theorem, we know that angle A is half the measure of arc BC, while angle B is half the measure of arc CD. Since the sum of arcs BC and CD is the entire circumference of the circle, we can conclude that arcs BC and CD are supplementary.
Therefore, angle A and angle B are also supplementary. By the same reasoning, angles C and D are supplementary as well. Hence, in an inscribed quadrilateral, opposite angles are always supplementary.