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The circle has center OO, and the measure of angle ∠POQ\angle POQ is 45%45\%. The length of minor arc ACAC is what fraction of the circumference of the circle? The number of degrees of arc in a circle is 360360.

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Q. The circle has center OO, and the measure of angle ∠POQ\angle POQ is 45%45\%. The length of minor arc ACAC is what fraction of the circumference of the circle? The number of degrees of arc in a circle is 360360.
  1. Understand Relationship: Understanding the relationship between the central angle and arc length.\newlineThe length of an arc is proportional to the measure of the central angle that subtends it. Since the measure of angle POQPOQ is 4545 degrees, the arc ACAC subtended by this angle is 45360\frac{45}{360} of the entire circumference of the circle.
  2. Calculate Fraction: Calculating the fraction of the circumference that arc AC represents.\newlineTo find the fraction of the circumference that arc AC represents, we divide the measure of the angle POQ by the total number of degrees in a circle.\newlineFraction of circumference = Measure of angle POQ / Total degrees in a circle\newlineFraction of circumference = Measure of angle POQTotal degrees in a circle\frac{\text{Measure of angle POQ}}{\text{Total degrees in a circle}}\newlineFraction of circumference = 45 degrees360 degrees\frac{45 \text{ degrees}}{360 \text{ degrees}}\newlineFraction of circumference = 18\frac{1}{8}

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