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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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04 Feb 2014, 01:46
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The Official Guide For GMAT® Quantitative Review, 2ND Edition

Attachment:

Untitled.png [ 21.06 KiB | Viewed 16094 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 [?]: 132977 [0], given: 12391

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

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04 Feb 2014, 01:46

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 [ 21.66 KiB | Viewed 15662 times ]
Therefore, the measure of angle ABC is 3 times 40°, so 120°. Sufficient.

Similar question to practice: what-is-the-measure-of-angle-yqz-in-the-figure-146476.html
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Re: In the figure above, what is the measure of angle ABC? [#permalink]

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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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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

Thanks

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

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07 Jan 2017, 03:38
girishraghu91 wrote:
Hi why cannot we assume angle XBC as 90 degree that would help us solve the question and the answer would be B

Thanks

Why would you assume that angle XBC is 90 degrees? There is absolutely no indication on this.
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In the figure above, what is the measure of angle ABC? [#permalink]

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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

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angles.jpg [ 12.11 KiB | Viewed 2274 times ]

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

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

B gives the value of x.

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