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In the figure above, with B a point on the line AC, what is the measu

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In the figure above, with B a point on the line AC, what is the measu  [#permalink]

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New post 01 Aug 2016, 05:44
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A
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C
D
E

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In the figure above, with B a point on the line AC, what is the measure of ∠XBZ? (Figure not necessarily drawn to scale.)

(1) BX bisects ∠ABY, which is a right angle, and BZ bisects ∠YBC.

(2) ∠ABX = ∠XBY = ∠YBZ = ∠ZBC

Attachment:
2016-08-01_1643.png
2016-08-01_1643.png [ 2.59 KiB | Viewed 1229 times ]

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In the figure above, with B a point on the line AC, what is the measu  [#permalink]

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New post 01 Aug 2016, 09:23
Bunuel wrote:
Image
In the figure above, with B a point on the line AC, what is the measure of ∠XBZ? (Figure not necessarily drawn to scale.)

(1) BX bisects ∠ABY, which is a right angle, and BZ bisects ∠YBC.

(2) ∠ABX = ∠XBY = ∠YBZ = ∠ZBC

Attachment:
2016-08-01_1643.png


Answer is D.

Since, AC is a line, so if ∠ABY = 90, then ∠CBY is also equal to 90.

Now, we have two bisectors of each given, this means each angle is 45 degrees. Thus, A is sufficient.

in B, we are already given each angle equal. Thus, 180/4=45 degree is the value of each angle. hence sufficient.
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Re: In the figure above, with B a point on the line AC, what is the measu  [#permalink]

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New post 01 Aug 2016, 11:23
Bunuel wrote:
Image
In the figure above, with B a point on the line AC, what is the measure of ∠XBZ? (Figure not necessarily drawn to scale.)

(1) BX bisects ∠ABY, which is a right angle, and BZ bisects ∠YBC.

(2) ∠ABX = ∠XBY = ∠YBZ = ∠ZBC

Attachment:
The attachment 2016-08-01_1643.png is no longer available

Refer attached fig.
i divided angle for ease of understanding as shown
ABX=1;XBY=2;YBZ=3 and ZBC=4

(1)Given ABY=90
So YBC=90 (As ABY+YBC=180)
BX bisects ABY=90=ABX+XBY=45 each
similarly BZ bisects YBC=90=YBZ+ZBC=45 each
all 1,2,3,4 angles are 45.
so XBZ=2+3=90Deg.
suff...
(2) ABC=180 and divided by 4 equal angles
1,2,3 &4=45 Deg.
same info as (1)
so XBZ=2+3=90Deg.
suff....

Ans D
Attachments

2016-08-01_1643.png
2016-08-01_1643.png [ 3.61 KiB | Viewed 1073 times ]

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Re: In the figure above, with B a point on the line AC, what is the measu  [#permalink]

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New post 13 Jan 2019, 05:23
Hi Bunuel,

my doubt in statement 1 is, what if the line from B to C was not a straight line and hence the angle YBC will not be 90, so how can statement 1 be sufficeint?
Please help

Thankyou
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Re: In the figure above, with B a point on the line AC, what is the measu  [#permalink]

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New post 13 Jan 2019, 09:05
yashna36 wrote:
Hi Bunuel,

my doubt in statement 1 is, what if the line from B to C was not a straight line and hence the angle YBC will not be 90, so how can statement 1 be sufficeint?
Please help

Thankyou


OFFICIAL GUIDE:

Problem Solving
Figures: All figures accompanying problem solving questions are intended to provide information useful in solving the problems. Figures are drawn as accurately as possible. Exceptions will be clearly noted. Lines shown as straight are straight, and lines that appear jagged are also straight. he positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero. All figures lie in a plane unless otherwise indicated.

Data Sufficiency:
Figures:
• Figures conform to the information given in the question, but will not necessarily conform to the additional information given in statements (1) and (2).
• Lines shown as straight are straight, and lines that appear jagged are also straight.
• The positions of points, angles, regions, etc., exist in the order shown, and angle measures are greater than zero.
• All figures lie in a plane unless otherwise indicated.[/quote]
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Re: In the figure above, with B a point on the line AC, what is the measu   [#permalink] 13 Jan 2019, 09:05
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