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The sum of angles 1, 2, 3, 4, 5 and 6 is

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Bunuel
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The sum of angles 1, 2, 3, 4, 5 and 6 is [#permalink] New post   31 Oct 2017, 10:14
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A
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Question Stats:

85% (00:33) correct 15% (00:46) wrong based on 92 sessions
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The sum of angles 1, 2, 3, 4, 5 and 6 is

(A) 180°
(B) 360°
(C) 480°
(D) 540°
(E) 720°

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The sum of angles 1, 2, 3, 4, 5 and 6 is [#permalink] New post   01 Nov 2017, 10:13
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Triangle AEC+Triangle BFD=180+180=360
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Re: The sum of angles 1, 2, 3, 4, 5 and 6 is [#permalink] New post   31 Oct 2017, 11:28
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Bunuel wrote:

The sum of angles 1, 2, 3, 4, 5 and 6 is

(A) 180°
(B) 360°
(C) 480°
(D) 540°
(E) 720°

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Attachment:
2017-10-31_2113.png


angle (2 + 4+ 6) + angle(1+3+5) = 180 +180

The sum of angles 1, 2, 3, 4, 5 and 6 is 360 (B) IMO.
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LevanKhukhunashvili
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Re: The sum of angles 1, 2, 3, 4, 5 and 6 is [#permalink] New post   11 May 2018, 04:39
The crucial moment is to see two triangles with distinct angles ACE & BCF
Sum of the angles of a triangle is 180
Sum of the angles of two triangles - 360

Ans - B
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The sum of angles 1, 2, 3, 4, 5 and 6 is [#permalink] New post   11 May 2018, 14:42
For those who struggle to see the triangles disscused by guys above:

Sum of angles of hexagon = 180 (6-2) = 720

Average of angles = 720/6 = 120. Then the average of each 2 base angles of small triangles will be 180-120=60.
Hence the Sum of (1+2+3+4+5+6) = 60*6 = 360 Answer (B)
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Re: The sum of angles 1, 2, 3, 4, 5 and 6 is [#permalink] New post   14 May 2018, 16:45
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Bunuel wrote:

The sum of angles 1, 2, 3, 4, 5 and 6 is

(A) 180°
(B) 360°
(C) 480°
(D) 540°
(E) 720°

Show Spoiler
Attachment:
2017-10-31_2113.png



We see that angle 1 + angle 3 + angle 5 = 180° since they are three angles of triangle ACE. Similarly, angle 2 + angle 4 + angle 6 = 180° since they are three angles of triangle BDF. Thus, the sum of these 6 angles is 180° + 180° = 360°.

Answer: B
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Re: The sum of angles 1, 2, 3, 4, 5 and 6 is [#permalink]
14 May 2018, 16:45
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