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In the figure above, if m is parallel to n, and a = 40, then b + c + d

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In the figure above, if m is parallel to n, and a = 40, then b + c + d [#permalink]

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New post 01 Aug 2017, 04:01
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In the figure above, if m is parallel to n, and a = 40, then b + c + d + e =

(A) 140
(B) 160
(C) 200
(D) 360
(E) 560


[Reveal] Spoiler:
Attachment:
2017-08-01_1350_001.png
2017-08-01_1350_001.png [ 5.82 KiB | Viewed 421 times ]
[Reveal] Spoiler: OA

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In the figure above, if m is parallel to n, and a = 40, then b + c + d [#permalink]

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New post 01 Aug 2017, 05:59
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If a=40, b=c=140
because sum of angles in a straight line is 180 degree(a+b=180 and a+c=180)

Because m || n, we can say that b=d and c=e(corresponding angles)
Therefore, b+c+d+e = 2(b+c) = \(2(140+140) = 2(280) = 560\)(Option E)
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Re: In the figure above, if m is parallel to n, and a = 40, then b + c + d [#permalink]

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New post 01 Aug 2017, 07:10
Bunuel wrote:
Image
In the figure above, if m is parallel to n, and a = 40, then b + c + d + e =

(A) 140
(B) 160
(C) 200
(D) 360
(E) 560


[Reveal] Spoiler:
Attachment:
2017-08-01_1350_001.png


from the figure above it is clear :
b=c

Also b=d ( angle made by a line on parallel lines)

also d=e
combining all three equations
b=c=d=e--------------------- equation (A)


also from the figure a+b=180 =>b=180-40=140
b+c+d+e=4 b (using equation (A)
b+c+d+e=4*140=560

hence (E)
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Re: In the figure above, if m is parallel to n, and a = 40, then b + c + d [#permalink]

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New post 02 Aug 2017, 12:33
Bunuel wrote:
Image
In the figure above, if m is parallel to n, and a = 40, then b + c + d + e =

(A) 140
(B) 160
(C) 200
(D) 360
(E) 560


[Reveal] Spoiler:
Attachment:
2017-08-01_1350_001.png


Since angle a is 40, angle b = 180 - 40 = 140, and angle c also = 140. Since angle b is equal to angle d and angle c is equal to angle e (each pair of these angles are corresponding angles), then angles d and e are also each equal to 140.

Thus, b + c + d + e = 140 x 4 = 560.

Answer: E
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Kudos [?]: 981 [0], given: 5

Re: In the figure above, if m is parallel to n, and a = 40, then b + c + d   [#permalink] 02 Aug 2017, 12:33
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In the figure above, if m is parallel to n, and a = 40, then b + c + d

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