Ohio Assessments for Educators (OAE) Mathematics Practice Exam

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What is the relationship between a central angle and an arc?

  1. The arc measurement is equal to the central angle

  2. The arc measurement is double the angle measurement

  3. The arc measurement is half the angle measurement

  4. The central angle is always larger than the arc

The correct answer is: The arc measurement is double the angle measurement

The relationship between a central angle and the arc it intercepts is defined in terms of degrees. A central angle is the angle whose vertex is at the center of a circle and whose sides (rays) extend to the circumference of the circle, effectively dividing the circle into two arcs. The measure of the arc that lies between the two endpoints of the rays of the central angle is directly proportional to the measure of that angle. The correct statement regarding this relationship is that the arc measurement is equal to the measure of the central angle. Therefore, when a central angle measures x degrees, the intercepted arc also measures x degrees. This understanding is crucial in geometry as it helps to determine properties related to circles, angles, and arcs effectively.

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