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In the figure above, x + y = : Problem Solving (PS)
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# In the figure above, x + y =

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