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# What is the value of a + b + c + d?

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Math Expert
Joined: 02 Sep 2009
Posts: 55231
What is the value of a + b + c + d?  [#permalink]

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17 Sep 2018, 01:44
1
1
00:00

Difficulty:

35% (medium)

Question Stats:

54% (01:47) correct 46% (01:04) wrong based on 34 sessions

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What is the value of a + b + c + d?

(A) 240
(B) 320
(C) 360
(D) 500
(E) 540

Attachment:

Capture.JPG [ 17.15 KiB | Viewed 457 times ]

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Joined: 10 Jan 2013
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Concentration: General Management, Strategy
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Re: What is the value of a + b + c + d?  [#permalink]

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17 Sep 2018, 04:56
So the sum of exterior angles of a polygon = (n-2)×180

Therefore sum becomes 540

And a+b+c+d+40=540

And thus 500

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Re: What is the value of a + b + c + d?  [#permalink]

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17 Sep 2018, 05:12
1
Sum of exterior angles of a regular polygon = 360
a+b+c+d+40=360
a+b+c+d=320
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Re: What is the value of a + b + c + d?  [#permalink]

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17 Sep 2018, 05:47
1
Bunuel wrote:

What is the value of a + b + c + d?

(A) 240
(B) 320
(C) 360
(D) 500
(E) 540

Attachment:
Capture.JPG

In terms of interior angles:

The sum of interior angles of an n-sided polygon = (n - 2)*180 = (5-2)*180 = 3*180 degrees

The interior angles are supplementary to angles a, b, c, d and 40 degrees.
180 - a + (180 - b) + (180 - c) + (180 - d) + (180 - 40) = 3*180
a + b + c + d = 320 degrees

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Re: What is the value of a + b + c + d?   [#permalink] 17 Sep 2018, 05:47
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