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The circle has center OO, and the measure of angle ROSROS is 150150 degrees. The length of minor arc RSRS is what fraction of the circumference of the circle? (The number of degrees of arc in a circle is 360360.)

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Full solution

Q. The circle has center OO, and the measure of angle ROSROS is 150150 degrees. The length of minor arc RSRS is what fraction of the circumference of the circle? (The number of degrees of arc in a circle is 360360.)
  1. Calculate Angle Fraction: Determine the fraction of the circle represented by a 150150-degree angle. Since a full circle is 360360 degrees, the fraction for the angle is 150360\frac{150}{360}.
  2. Simplify Fraction: Simplify the fraction 150360\frac{150}{360} to its lowest terms. Divide both the numerator and the denominator by their greatest common divisor, which is 3030. So, 150÷30=5150 \div 30 = 5 and 360÷30=12360 \div 30 = 12. The simplified fraction is 512\frac{5}{12}.
  3. Conclude Arc Length: Conclude that the length of minor arc RSRS is 512\frac{5}{12} of the circle's total circumference, since the arc length fraction is directly proportional to the angle fraction.

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