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# In the figure above, what is the value of x in terms of a, b and y?

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Math Expert
Joined: 02 Sep 2009
Posts: 53063
In the figure above, what is the value of x in terms of a, b and y?  [#permalink]

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08 Aug 2017, 09:40
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Difficulty:

15% (low)

Question Stats:

80% (01:19) correct 20% (02:06) wrong based on 59 sessions

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In the figure above, what is the value of x in terms of a, b and y?

(A) a + b
(B) 2a + 2b
(C) 2y
(D) y + a + b
(E) y – a – b

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2017-08-08_2139.png [ 7.53 KiB | Viewed 1862 times ]

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Re: In the figure above, what is the value of x in terms of a, b and y?  [#permalink]

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08 Aug 2017, 10:22

We know that the sum of angles in a triangle is 180 degree.
In bigger triangle, y + 2a + 2b = 180

Similarly, x + a + b = 180 degree in the smaller triangle.
Multiplying by 2, we get 2x + 2a + 2b = 360
Therefore, 2x + 180 - y = 360 => 2x = 180 + y

But we know that x = 180 - (a+b)

So 2x = 180 + y => x + 180 - (a+b) = 180 + y
x = y + a + b(Option D)
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Joined: 23 Jul 2015
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Re: In the figure above, what is the value of x in terms of a, b and y?  [#permalink]

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08 Aug 2017, 22:46

y + 2a + 2b = 180 ... (i)

x = 180 - a - b ... (ii)
substituting (i) in (ii)
x = y + 2a + 2b - a - b
x = y + a + b (choice D)
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Joined: 11 Mar 2015
Posts: 34
Re: In the figure above, what is the value of x in terms of a, b and y?  [#permalink]

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16 Dec 2017, 08:28
Here, 2a+2b+y=180.............(1)
a+b+x=180................(2)
So, 2a+2b+y=a+b+x
=>x=y+a+b
Re: In the figure above, what is the value of x in terms of a, b and y?   [#permalink] 16 Dec 2017, 08:28
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