Point O is the center of a circle. The measure of arc RS on this circle is 100°. What is the measure, in degrees, of its associated angle ROS ?
Correct answer: A. 100
- A. 100
- B. 60
- C. 40
- D. 10
Explanation
The correct answer is 100. It's given that point O is the center of a circle and the measure of arc RS on the circle is o 100 . It follows that points R and S lie on the circle. Therefore, OR and OS are radii of the circle. A central angle is an angle n formed by two radii of a circle, with its vertex at the center of the circle. Therefore,∠ ROS is a central angle. Because the degree measure of an arc is equal to the measure of its associated central angle, it follows that the measure, in degrees, of ∠ ROS is 100.
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Quantitative reasoning applies arithmetic and basic algebra to numerical relationships, including percentages, ratios, averages, fractions, proportions, profit and loss, rates, time, work and measurement. Questions focus on translating words into equations, choosing an efficient method and checking whether the result is numerically reasonable.
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