Angles in a Semicircle and Cyclic Quadrilaterals

Angle in a semicircle

Theorem: Any angle in a semicircle (subtended by the diameter) is exactly 90° - always, no matter where on the arc the point sits.

Cyclic quadrilaterals

A quadrilateral with all four corners on the circle. Theorem: opposite angles add up to 180° - like two see-saws balancing each other out.

Example: In a cyclic quadrilateral, one angle is 110°. The opposite angle is 180 - 110 = 70°.

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