The value of the angles mAC = 100 and ∠ABC = 50. The measure of each inscribed angle is exactly half the measure of its intercepted arc.
What is an inscribed circle?
The greatest circle that can be drawn inside a regular, cyclic polygon is known in geometry as an inscribed circle, also known as the incircle of a polygon.
The vertex of an inscribed angle can be anywhere on the circle as long as its sides intersect the circle to form an intercepted arc. The Inscribed Angle Theorem states that the measure of an inscribed angle is half the measure of its intercepted arc. Inscribed angles that intercept the same arc are congruent.
In a circle, two inscribed angles with the same intercepted arc are congruent. Proof: The measure of each inscribed angle is exactly half the measure of its intercepted arc. Since they have the same intercepted arc, they have the same measure.
Therefore, the measure of each inscribed angle is exactly half the measure of its intercepted arc.
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