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In the figure above, what is the measure of angle ABC?

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In the figure above, what is the measure of angle ABC? [#permalink]

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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:
Untitled.png
Untitled.png [ 21.06 KiB | Viewed 15310 times ]
In the figure above, what is the measure of angle ABC?

(1) BX bisects angle ABY and BY bisects angle XBC.
(2) The measure of angle ABX is 40°.

Data Sufficiency
Question: 72
Category: Geometry Angles
Page: 158
Difficulty: 600


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Kudos [?]: 128912 [0], given: 12183

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Re: In the figure above, what is the measure of angle ABC? [#permalink]

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New post 04 Feb 2014, 01:46
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In the figure above, what is the measure of angle ABC?

(1) BX bisects angle ABY and BY bisects angle XBC. We don't have any numerical value. Not sufficient.

(2) The measure of angle ABX is 40°. We don't have relationship between angle ABX and angle ABC. Not sufficient.

(1)+(2) When we combine the statements we have the following case:
Attachment:
Untitled.png
Untitled.png [ 21.66 KiB | Viewed 15055 times ]
Therefore, the measure of angle ABC is 3 times 40°, so 120°. Sufficient.

Answer: C.

Similar question to practice: what-is-the-measure-of-angle-yqz-in-the-figure-146476.html
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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

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Re: In the figure above, what is the measure of angle ABC? [#permalink]

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New post 04 Feb 2014, 06:27
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St1) Angle ABX = Angle XBY = Angle YBC --> not sufficient
St2) AngleABX = 40 --> not sufficient

From 1 + 2, Angle ABC = 3 Angle ABX = 3 * 40 = 120 --> suff

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Re: In the figure above, what is the measure of angle ABC? [#permalink]

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New post 06 Jan 2017, 08:31
Hi why cannot we assume angle XBC as 90 degree that would help us solve the question and the answer would be B
Please explain

Thanks

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Re: In the figure above, what is the measure of angle ABC? [#permalink]

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In the figure above, what is the measure of angle ABC? [#permalink]

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New post 03 Jul 2017, 09:26
I like to redraw the diagram

Statement 1: From the figure you can see that this can be interpreted in many ways. Depending on how you draw the lines, \(\angle ABC\) can take many values.........Insufficient

Stament 2: This statement tells us that \(\angle ABX\) = \(40^{\circ}\) No information about anything else.........Insufficient

From (1) and (2) \(\angle ABX\) = \(40^{\circ}\) and bisecting lines
This means \(\angle XBY\) = \(40^{\circ}\) and \(\angle YBC\) = \(40^{\circ}\) , hence \(\angle ABC\) = \(120^{\circ}\)............Sufficient

Answer is C
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Re: In the figure above, what is the measure of angle ABC? [#permalink]

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New post 06 Jul 2017, 12:14
All angles equal x.
Therefore the sum of the angle is 3x.

B gives the value of x.

The answer is thus C.
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Kudos [?]: 41 [0], given: 267

Re: In the figure above, what is the measure of angle ABC?   [#permalink] 06 Jul 2017, 12:14
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