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A central angle is an angle whose vertex is at the center of the circle. It intersects the circle at two points and its measure is equal to the arc length it intercepts on the circle.
An inscribed angle is an angle whose vertex is on the circle and its sides intersect the circle at two different points. Inscribed angles are half the measure of the central angle that intercepts the same arc.
The measure of an inscribed angle is half the measure of its intercepted arc. This is known as the inscribed angle theorem.
The measure of a central angle or an inscribed angle can be found by using the central angle theorem or the inscribed angle theorem. These theorems state that the measure of an angle is equal to the ratio of its intercepted arc to the entire circumference of the circle, multiplied by 360 degrees.
In a cyclic quadrilateral, opposite angles are supplementary, meaning they add up to 180 degrees. This is known as the opposite angles theorem.
