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

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

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New post 24 Aug 2017, 23:46
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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


Attachment:
2017-08-25_1041_001.png
2017-08-25_1041_001.png [ 18.09 KiB | Viewed 1576 times ]

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Re: In the figure above, what is the average (arithmetic mean) degree meas [#permalink]

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New post 25 Aug 2017, 11:12
Bunuel wrote:
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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


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.

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

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New post 25 Aug 2017, 11:21
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Let's call the point of intersection of the 6 triangles 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 \(\frac{240}{6} = 40\)
Since the sum of angles in a triangle is 180, the sum of the other 2 angles in each of the triangles is 140.

Therefore, the average degree measure is \(\frac{140*6}{12} =\) 70(Option D)
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Re: In the figure above, what is the average (arithmetic mean) degree meas [#permalink]

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New post 20 Apr 2018, 10:47
We know that a full circle on a flat plane is 360 degrees.
Since 120 degrees are accounted for the total for the centerpoint angles on the 6 triangles shown must be 240
240/6= 40
Therefore we know that on average one angle of each of the triangles is 40.
Because triangle angles must sum to 180, we know that on average the sum of the other two angles for each triangle is 140. Divide 140 by 2 angles and we can say that on average, the listed angles are 70 degrees!
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In the figure above, what is the average (arithmetic mean) degree meas [#permalink]

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New post 20 Apr 2018, 12:39
Sum of angles of heptagon (7 sided polygon) = 180*(7-2)= 900
Sum of 2 angles of the triangle x+y= 180-120 = 60, so the sum of rest 12 angles = 900-60 = 840 and Av = 840/12 = 70

Answer (D)
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In the figure above, what is the average (arithmetic mean) degree meas   [#permalink] 20 Apr 2018, 12:39
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