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

Question

https://gmatclub.com/forum/download/file.php?id=22252 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°. Untitled.png

Bunuel · Answer

https://gmatclub.com/forum/download/file.php?id=22252 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: Untitled.png 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

syamen · Answer

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

girishraghu91 · Answer

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

Bunuel · Answer

Why would you assume that angle XBC is 90 degrees? There is absolutely no indication on this.

sasyaharry · Answer

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

Shiv2016 · Answer

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

B gives the value of x.

The answer is thus C.

Khaleesi700 · Answer

(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

jacobkeung · Answer

Doesn't 'bisect' mean the line comes in at a 45 degree angle? Therefore, if both lines bisect then each segment is 45 degrees?

Basshead · Answer

Bisect  means to divide into two parts.

Combining the two statements, we know ABX = 40. If ABX = XBY = YBC, each angle equals 40 degrees.

40 * 3 = 120 degrees

bumpbot · Answer

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

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