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# In the figure above, what is the average (arithmetic mean) degree meas

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Math Expert
Joined: 02 Sep 2009
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In the figure above, what is the average (arithmetic mean) degree meas [#permalink]

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24 Aug 2017, 22:46
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In the figure above, what is the average (arithmetic mean) degree measure of the 12 marked angles?

(A) 40
(B) 50
(C) 60
(D) 70
(E) cannot be determined from the given information

[Reveal] Spoiler:
Attachment:

2017-08-25_1041_001.png [ 18.09 KiB | Viewed 1235 times ]
[Reveal] Spoiler: OA

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Manager
Joined: 27 Dec 2016
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Concentration: Social Entrepreneurship, Nonprofit
GPA: 3.65
WE: Sales (Consumer Products)
Re: In the figure above, what is the average (arithmetic mean) degree meas [#permalink]

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25 Aug 2017, 10:12
Bunuel wrote:

In the figure above, what is the average (arithmetic mean) degree measure of the 12 marked angles?

(A) 40
(B) 50
(C) 60
(D) 70
(E) cannot be determined from the given information

[Reveal] Spoiler:
Attachment:
2017-08-25_1041_001.png

- Total angles who meet in the centre should be 360-120 = 240.
- IF we assume that the centre angle of each triangle IS SAME, we can calculate the average.
- However, we can assume anything from given picture, so we can calculate.

E.

Waiting great explanation from Bunuel
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In the figure above, what is the average (arithmetic mean) degree meas [#permalink]

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25 Aug 2017, 10:21
2
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Lets call the point O, around which the sum of the angles is 360
Since, the angle given is 120 degree, the remainder of the angles is 240.
There are 6 triangles and the angle(in each of the 6 triangles around point O) is around $$\frac{240}{6} = 40$$

Since the sum of angles in a triangle is 180, the other 2 angles in each of the triangles
have a sum of 140. Hence, the average degree measure is $$\frac{140*6}{12} = 70$$

Therefore, the average degree measure is 70(Option D)
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In the figure above, what is the average (arithmetic mean) degree meas   [#permalink] 25 Aug 2017, 10:21
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