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Mathematics

Grade9

Easy

Question

In the figure below, the radius of circle P is 10 units. The arc length of $stack A B C with overbrace on top$ is 16 $pi$ .

What is the arc measure of $stack A C with overbrace on top$ , in degrees?

72°
288°
$4 π$
$20 π$

hint Hint:

Arc length = $fraction numerator theta over denominator 360 end fraction cross times 2 cross times pi cross times r$

The correct answer is: 72°

Lets find the length of arc AC.
Length of arc AC = circumference – length of arc ABC = $2 cross times pi cross times 10$ - $16 pi$ = $4 pi$
Length of arc AC = ( $fraction numerator a r c blank a n g l e over denominator 360 end fraction$ ) $cross times$ circumference
Arc Angle = $fraction numerator 4 pi cross times 360 over denominator 20 pi end fraction$ = 72°

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