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

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

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29 Nov 2015, 10:48
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5% (low)

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91% (00:41) correct 9% (00:43) wrong based on 64 sessions

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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

Attachment:

Isosceles_Pair.png [ 6.71 KiB | Viewed 1575 times ]

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Re: Triangles ABC and BCD are each isosceles. If a = 40, what is the value  [#permalink]

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29 Nov 2015, 10:55
a = 40
a + 2x = 180 --> x = 70

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

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

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29 Nov 2015, 11:37
In $$\triangle$$ ABC ,
=> a +2x= 180
Since a=40
x= 70

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

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Joined: 02 Sep 2009
Posts: 47918
Re: Triangles ABC and BCD are each isosceles. If a = 40, what is the value  [#permalink]

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01 Jan 2018, 11:50
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

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 &nbs [#permalink] 01 Jan 2018, 11:50
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