Central Angle Theorem

Move points A and B around the circle to explore the relationships between inscribed and central angles. Please note that angle measures and arcs are both measured in degrees. Use the diagram to answer the following questions:

Central Angles and Intercepted Arcs

The measurement of a central angle is always the same as the measure of the arc subtended by the central angle. For any two points on a circle there is always one arc measure and one central angle measure that are identical. We say that the arc intercepts the circle at the two points. An inscribed angle intercepts (or intersects) the circle at the two points that are not the inscribed angle's vertex

1. Find the inscribed angle measure

If mAOB = 196°, find the measure of major arc AXB

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2. Find the inscribed angle measure

If the mAOB = 80°, find the mACB

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3. Find the intercepted arc measure

If the mACB = 50°, find the measure of minor arc AB

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