Point O is the center of a circle. The measure of arc R S on this circle is 100 °

Question

Point O is the center of a circle. The measure of arc R S on this circle is 100 &#176; . What is the measure, in degrees, of its associated angle R O S ?

Accepted Answer

The correct answer is 100 . It's given that point O is the center of a circle and the measure of arc R S on the circle is 100 /mo> . It follows that points R and S lie on the circle. Therefore, O R /mo> and O S /mo> are radii of the circle. A central angle is an angle formed by two radii of a circle, with its vertex at the center of the circle. Therefore, R O S 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 R O S is 100 .

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