Inscribed Angle Calculator

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Explore the relationship between inscribed angles and their intercepted arcs in a circle. Discover how arcs define internal angles.

Circle Geometry

Inscribed Angle (degrees)

Intercepted Arc (degrees)

Geometric Verification

30.0°degrees

Angle Measure

Arc Measure60.0°

Relationship1 : 2

Angle (30°) = 1/2 × Arc (60°)

About this calculator

The Inscribed Angle Theorem

An inscribed angle is an angle formed by two chords in a circle that have a common endpoint on the circle. The intercepted arc is the portion of the circle between the chord's other endpoints. The measure of an inscribed angle is exactly half the measure of its intercepted arc.

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Pro Tips

Inscribed in Same Arc: All inscribed angles that intercept the same arc are equal.
Semicircle: An angle inscribed in a semicircle is ALWAYS a right angle (90°).
Central Angle: A central angle is exactly twice the measure of an inscribed angle that intercepts the same arc.

Fun Facts

"This theorem is a fundamental part of Euclidean geometry."
"Angles inscribed in the same arc are equal, regardless of where the vertex is located on the arc."
"The theorem was known to ancient Greek mathematicians like Thales of Miletus."

Formula: Angle = 1/2 × Arc