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01 Aug 2016, 05:44
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D
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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 [ 2.59 KiB | Viewed 7261 times ]
01 Aug 2016, 09:23
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Bunuel
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.
01 Aug 2016, 11:23
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Bunuel
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
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2016-08-01_1643.png [ 3.61 KiB | Viewed 4258 times ]
