WEBVTT
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A circle has a circumference of 16π units.
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Find, in degrees, the measure of the central angle of an arc with a length of three π units.
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To solve this question, we need to think about the relationship between the arc length and circumference and the central angle of that arc.
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If we take the ratio of the arc length over the circumference, it will be equal to the relationship between the central angle and a full rotation.
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The full rotation will either be 360 degrees or two π, depending on whether weβre working in degrees or radians.
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In this case, we want to find the angle in degrees.
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So weβll substitute 360 degrees for our full rotation.
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The arc length is three π units, and the circumference is 16π units.
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If we let our central angle be π, we have π over 360 is equal to three π over 16π.
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We can simplify a little bit.
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The π in the numerator and the π in the denominator cancel out.
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We canβt reduce three over 16 any further.
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So we multiply both sides of the equation by 360 degrees.
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And weβll have π is equal to three times 360 degrees divided by 16.
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When we do that, we get 67.5 degrees.