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14 August, 16:16

In the figure below, the radius of circle P is 10 units. The arc length of ABC is 16 pi. What is the arc measure of AC, in degrees?

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  1. 14 August, 20:12
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    72 degrees

    Step-by-step explanation:

    We need to know the total circumference in order to determine the arc measure for ABC before we figure out AC

    Circumference = 2πr → = 2π (10) → = 20π

    We know the length of ABC

    so we set up a proportion to figure out its arc measure.

    arc length / circumference = arc measure / degrees in a circle

    16π / 20π = arc measure / 360 degrees

    arc measure = 360 x 16π / 20π = 228 degrees

    The arc measure of ABC is 228 degrees

    If we combine the major arc ABC, and the minor arc AC we have the entire circle.

    288 degrees + m AC = 360

    m AC = 72 degrees

    The measure of AC is 72 degrees

    (i got the explanation off of Klan Academy when i answered the question)
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