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

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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
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Re: In the figure above, what is the measure of angle ABC? [#permalink]
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girishraghu91
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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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

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Re: In the figure above, what is the measure of angle ABC? [#permalink]
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]
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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]
Doesn't 'bisect' mean the line comes in at a 45 degree angle? Therefore, if both lines bisect then each segment is 45 degrees?
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Re: In the figure above, what is the measure of angle ABC? [#permalink]
jacobkeung
Doesn't 'bisect' mean the line comes in at a 45 degree angle? Therefore, if both lines bisect then each segment is 45 degrees?

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
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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]
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