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Triangles ABC and BCD are each isosceles. If a = 40, what is the value

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Bunuel
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Triangles ABC and BCD are each isosceles. If a = 40, what is the value [#permalink] New post   29 Nov 2015, 10:48
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Triangles ABC and BCD are each isosceles. If a = 40, what is the value of y?

A. 40
B. 45
C. 50
D. 55
E. 60

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D
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Re: Triangles ABC and BCD are each isosceles. If a = 40, what is the value [#permalink] New post   29 Nov 2015, 10:55
a = 40
a + 2x = 180 --> x = 70

x + 2y = 180 --> y = 55

Answer: D
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Triangles ABC and BCD are each isosceles. If a = 40, what is the value [#permalink] New post   29 Nov 2015, 11:37
In \(\triangle\) ABC ,
=> a +2x= 180
Since a=40
x= 70

In \(\triangle\) BCD,
=>x+2y =180
=>y=55

Answer D
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Re: Triangles ABC and BCD are each isosceles. If a = 40, what is the value [#permalink] New post   01 Jan 2018, 11:50
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Bunuel wrote:

Triangles ABC and BCD are each isosceles. If a = 40, what is the value of y?

A. 40
B. 45
C. 50
D. 55
E. 60

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Attachment:
Isosceles_Pair.png


VERITAS PREP OFFICIAL SOLUTION:

One extremely helpful tool that you’ll often find in your geometry toolkit is the presence of isosceles triangles. Here, once you’ve filled in 40 for angle a, you should notice that even though there are two angles remaining to solve for within triangle ABC, those two angles each equal the same thing. So since the sum of all three has to be 180, and angle a already accounts for 40, 2x has to equal the remaining 140. 2x = 140 means that x = 70. And then you get to use the same logic all over again. Within triangle BCD, you know that x = 70 and that the sum of the three angles must be 180. That means that 2y = 110, so y = 55, answer choice D.
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Re: Triangles ABC and BCD are each isosceles. If a = 40, what is the value [#permalink] New post   31 May 2020, 08:08
In Tri. ABC, 2x+a = 180
2x = 180-40
2x = 140
x = 70

In Tri. BCD,
x+2y = 180
2y= 180-x
2y= 180-70
2y = 110
y = 55 (Ans)
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Re: Triangles ABC and BCD are each isosceles. If a = 40, what is the value [#permalink]
31 May 2020, 08:08
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