Assessment and Learning in Knowledge Spaces (ALEKS) Practice Exam

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Study for the ALEKS Exam with in-depth coverage. Utilize flashcards and multiple-choice questions with hints and explanations to get prepared!

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What is the relationship between a central angle and the arc it intercepts?

The measure of the arc is equal to the measure of the central angle
The arc is always longer than the central angle
The arc and central angle are always equal to 180 degrees
The arc measure varies independently from the central angle

The correct answer is: The measure of the arc is equal to the measure of the central angle

The measure of the arc is equal to the measure of the central angle. This relationship is fundamental in circle geometry. A central angle is formed by two radii of a circle that meet at the center, and the arc that it intercepts is the portion of the circle's circumference that lies between the two endpoints of the angle. Since the circle is divided based on the angle formed at the center, the measure of the arc directly corresponds to the degree measure of the central angle. For example, if the central angle measures 30 degrees, then the arc it intercepts will also measure 30 degrees. This concept is key in understanding various properties of circles, including calculations involving arc lengths and sectors. The other options misrepresent this relationship by suggesting that the arc could be longer than the angle, that both must equal a specific value like 180 degrees, or that they vary independently, none of which aligns with the established geometric principles.