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If the figure above shows part of a circle with arcs of length 3 and

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If the figure above shows part of a circle with arcs of length 3 and  [#permalink]

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New post 13 Sep 2018, 01:31
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If the figure above shows part of a circle with arcs of length 3 and a that alternate around the entire circumference so that there are a total of 36 such arcs, what is the degree measure of one arc of length a?

(1) The circumference of the circle is 90.
(2) The length of a is 2.


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image012.jpg
image012.jpg [ 2.08 KiB | Viewed 286 times ]

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If the figure above shows part of a circle with arcs of length 3 and  [#permalink]

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New post 13 Sep 2018, 02:16
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Bunuel wrote:
Image
If the figure above shows part of a circle with arcs of length 3 and a that alternate around the entire circumference so that there are a total of 36 such arcs, what is the degree measure of one arc of length a?

(1) The circumference of the circle is 90.
(2) The length of a is 2.


Attachment:
image012.jpg


36 such arcs i.e. 18 arcs of length 3 and 18 arcs of length a
i.e. Total Circumference\(= 18*(a+3) = 18a+54\)


Question: Degree measure of arc of length a = ?

Statement 1: The circumference of the circle is 90.
i.e. \(18*(a+3) = 18a+54=90\)
now \((Angle/360) = 36/90\)
i.e. Angle for all \(18a = 144\)
i.e. angle of \(a = 8º\)
SUFFICIENT

Statement 2: The length of a is 2
Using this also total circumference can be calculated
as \(18a+54 = 18*2+54 = 90\)
i.e. now \((Angle/360) = 36/90\)
i.e. Angle for all \(18a = 144\)
i.e. angle of \(a = 8º\)
SUFFICIENT

ANswer: Option D
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If the figure above shows part of a circle with arcs of length 3 and &nbs [#permalink] 13 Sep 2018, 02:16
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