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# A circle, in order, is divided into 8 consecutive arcs of 10, 20, 30

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Intern
Joined: 04 Jul 2018
Posts: 4
A circle, in order, is divided into 8 consecutive arcs of 10, 20, 30  [#permalink]

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29 Jan 2019, 11:44
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Difficulty:

65% (hard)

Question Stats:

44% (02:03) correct 56% (02:06) wrong based on 30 sessions

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A circle, in order, is divided into 8 consecutive arcs of 10º, 20º, 30º, ..., 80º respectively. If The eight points are connected to form an octagon, what is the measure of the largest angle of that octagon?
A. 100
B. 135
C. 150
D. 165
E. 170
Math Expert
Joined: 02 Aug 2009
Posts: 8007
A circle, in order, is divided into 8 consecutive arcs of 10, 20, 30  [#permalink]

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29 Jan 2019, 19:32
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dreamerchaser wrote:
A circle, in order, is divided into 8 consecutive arcs of 10º, 20º, 30º, ..., 80º respectively. If The eight points are connected to form an octagon, what is the measure of the largest angle of that octagon?
A. 100
B. 135
C. 150
D. 165
E. 170

The arcs 10° to 80° add up to 360°, so when you join these points at the centre of the circle you will have 8 triangles with same angle as the measure of arc..
All these triangles will be isosceles as two side will be the radius. Angles made in arc of 10° will be 10, (180-10)/2,(180-10)/2.
Similarly the next triangle will have 20,(180-20)/2,(180-20)/2 and so on.

Now each angle of octagon will consist of two angles, one each from neighbouring triangle..
It will be largest when it consists of two largest angles, which will be subtended by two smallest arcs.
So the two next to each other should be 10° and 20° and the angle will be (180-10)/2+(180-20)/2=85+80=165

D
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Re: A circle, in order, is divided into 8 consecutive arcs of 10, 20, 30  [#permalink]

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29 Jan 2019, 22:16
chetan2u ,can you please explain using a diagram.
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Ankit
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Re: A circle, in order, is divided into 8 consecutive arcs of 10, 20, 30  [#permalink]

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29 Jan 2019, 22:41
chetan2u ,can you please explain using a diagram.

please check the figure above. If any queries, revert.
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Re: A circle, in order, is divided into 8 consecutive arcs of 10, 20, 30   [#permalink] 29 Jan 2019, 22:41
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