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# In the below figure, what is angle PBC? 1. ABCD is a square

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In the below figure, what is angle PBC? 1. ABCD is a square [#permalink]  13 Feb 2006, 15:48
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In the below figure, what is angle PBC?

1. ABCD is a square
2. PDC is an equilateral triangle
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Quadrilateral.jpg [ 7.39 KiB | Viewed 595 times ]

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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

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It is C.
From 1. We know only that all the sides are the same and angles are 90.
not suf.
From 2. angle PDC = DPC = CDP=60 not suf.

Together.
Angle PCB = 90-60=30,
PC=BC =>agle BPC = PBC=(180-30)/2=75
Suf.
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C. Both statements are sufficient together.

CP == CB
Angle CPB = 30 degrees

Angle PBC = (180-30)/2 = 75 degrees
CEO
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How can I be so silly.... you guys are rigjt.
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(i) and (ii) are clearly insufficient on their own.

Rule out A,B,D.

With (i) n (ii) together:

- If Triangle PDC is equilateral, PCD = 60 and PCB = 30 as its a square.
- Triangle PBC is Isoceles with the angle opp to base = 30
- The other 2 angles CPB and CBP are hence (180-30)/2 = 75

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ps_dahiya wrote:
:wall

How can I be so silly.... you guys are rigjt.
Did you try drawing it out yourself. That always helps me.
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Agree with everyone's working, PBC = 75 degrees. C
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not following [#permalink]  19 Feb 2006, 11:35
how did u guys come to the conclusion that triangle PBC is isoscles?
thanks
siva
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Re: not following [#permalink]  19 Feb 2006, 12:30
Avis wrote:
how did u guys come to the conclusion that triangle PBC is isoscles?
thanks
siva
ABCD is a square. pdc is an egquilateral triangle that shares a side with square ABCD. Sides DC aand BC are clearly equal since they are part of the same square. Side PC = DC = BC. PC and BC form the second triangle with an angle of 30 degrees. A 30 degree angle with 2 equal sides proves that it is an isosceles triangle.

Hope it helps. Not sure I explained very well. Try drawing it out. It makes it much easier. The innacurate drawing could really throw ppl off.
Re: not following   [#permalink] 19 Feb 2006, 12:30
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