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In the figure above, x + y =

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In the figure above, x + y =  [#permalink]

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New post 25 Dec 2018, 08:20
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

75% (01:13) correct 25% (01:02) wrong based on 76 sessions

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Re: In the figure above, x + y =  [#permalink]

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New post 25 Dec 2018, 09:11
Bunuel wrote:
Image
In the figure above, x + y =

A. 40
B. 120
C. 140
D. 180
E. 220


Attachment:
2018-12-25_1917.png


we can say
40+180-y+180-x=180

x+y= 220
IMO E
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Re: In the figure above, x + y =  [#permalink]

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New post 31 Jul 2019, 08:51
Top Contributor
Bunuel wrote:
Image
In the figure above, x + y =

A. 40
B. 120
C. 140
D. 180
E. 220


Attachment:
2018-12-25_1917.png


We know that the top angle must be 40°.
At the same time, let's call the other 2 angles a and b.
We know that a + b + 40 = 180 (since the 3 angles in a triangle must add to 180°)

Also, since angles on a line must add to 180°, we know that: a = 180-y and b = 180-x

We can now take a + b + 40 = 180 and replace a and b with their equivalent values.
We get: (180-y) + (180-x) + 40 = 180
Simplify: 400 - y - x = 180
Subtract 400 from both sides: -y - x = -220
Multiply both sides by -1 to get: x + y = 220

Answer: E

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Brent
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Re: In the figure above, x + y =  [#permalink]

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New post 05 Aug 2019, 17:16
Bunuel wrote:
Image
In the figure above, x + y =

A. 40
B. 120
C. 140
D. 180
E. 220


Attachment:
2018-12-25_1917.png


We can create the equation for the 3 interior angles of the triangle:

(180 - y) + (180 - x) + (180 - 140) = 180

220 = x + y

Alternate solution:

We know the sum of the measures of the exterior angles of any polygon is 360 degrees. Here, x, y, and 140 are the measures of the exterior angles of the triangle; therefore,

x + y + 140 = 360

x + y = 220

Answer: E
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Re: In the figure above, x + y =  [#permalink]

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New post 14 Aug 2019, 03:01
a + x = 180
y = 40 + a
a = 180 -x
y = 40 + 180 - x
y + x = 220
GMAT Club Bot
Re: In the figure above, x + y =   [#permalink] 14 Aug 2019, 03:01
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