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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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New post 29 Nov 2015, 10:48
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A
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C
D
E

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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
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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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]

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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]

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New post 01 Jan 2018, 11:50
Bunuel wrote:
Image
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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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

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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