Prove that the angles in a cyclic quadrilateral always sum up to 360 degrees, and detail how the properties of an inscribed angle of a circle can be used in this proof.
Answer 1
Michael Beck
In a cyclic quadrilateral, the opposite angles are supplementary. This is because each pair of opposite angles subtends the same arc, and the sum of angles subtending an arc equals 180 degrees. Therefore, the sum of all four angles in a cyclic quadrilateral is 360 degrees.
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