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Math Expert V
Joined: 02 Sep 2009
Posts: 60690
In the figure above, what is the measure of angle ABC?  [#permalink]

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Difficulty:   5% (low)

Question Stats: 87% (01:01) correct 13% (01:14) wrong based on 609 sessions

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The Official Guide For GMAT® Quantitative Review, 2ND Edition 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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Intern  Joined: 29 Oct 2013
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Re: In the figure above, what is the measure of angle ABC?  [#permalink]

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1
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
Math Expert V
Joined: 02 Sep 2009
Posts: 60690
Re: In the figure above, what is the measure of angle ABC?  [#permalink]

### Show Tags 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 25460 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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Intern  Joined: 13 Nov 2016
Posts: 1
Re: In the figure above, what is the measure of angle ABC?  [#permalink]

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Hi why cannot we assume angle XBC as 90 degree that would help us solve the question and the answer would be B

Thanks
Math Expert V
Joined: 02 Sep 2009
Posts: 60690
Re: In the figure above, what is the measure of angle ABC?  [#permalink]

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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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Manager  G
Joined: 22 Nov 2016
Posts: 230
Location: United States (CA)
GMAT 1: 640 Q43 V35
GPA: 3.4
WE: Design (Other)
Re: In the figure above, what is the measure of angle ABC?  [#permalink]

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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

Attachments angles.jpg [ 12.11 KiB | Viewed 12046 times ]

Director  G
Joined: 02 Sep 2016
Posts: 635
Re: In the figure above, what is the measure of angle ABC?  [#permalink]

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All angles equal x.
Therefore the sum of the angle is 3x.

B gives the value of x.

Intern  B
Joined: 15 Mar 2017
Posts: 7
Re: In the figure above, what is the measure of angle ABC?  [#permalink]

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(1) BX bisects angle ABY and BY bisects angle XBC------from this we can imply that -----angle ABX = angle XBY
and angle XBY=BYC but no value for angle given. Not sufficient we are left with option BCE

(2) The measure of angle ABX is 40°.

No relation given between rest of the angles. B out we are left with C and E

1+2---

if angle ABX = 40 = angle XBY = angle BYC......angle ABC= 3*40=120
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Re: In the figure above, what is the measure of angle ABC?  [#permalink]

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_________________ Re: In the figure above, what is the measure of angle ABC?   [#permalink] 28 Nov 2019, 09:33
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