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In the figure above, x + y =

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Joined: 02 Sep 2009
Posts: 60627
In the figure above, x + y =  [#permalink]

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25 Dec 2018, 08:20
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In the figure above, x + y =

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

Attachment:

2018-12-25_1917.png [ 10.49 KiB | Viewed 1356 times ]

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

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25 Dec 2018, 09:11
Bunuel wrote:

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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Joined: 12 Sep 2015
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Re: In the figure above, x + y =  [#permalink]

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31 Jul 2019, 08:51
Top Contributor
Bunuel wrote:

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

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

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05 Aug 2019, 17:16
Bunuel wrote:

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

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

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

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11 Oct 2019, 23:13
Bunuel wrote:

In the figure above, x + y =

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

Attachment:
2018-12-25_1917.png

An alternate approach would be to use the property that an exterior angle is the sum of the 2 opposite interior angles. In this case, the two bottom angles of the triangle can be written as $$180-x$$ and $$180-y$$.

$$180-x + 180-y = 140$$
$$360-140 = x+y$$
$$220 = x+y$$ (Ans. E)
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Re: In the figure above, x + y =   [#permalink] 11 Oct 2019, 23:13
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