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# ABCD is a quadrilateral. Is the sum of angles ABC and CDA is

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ABCD is a quadrilateral. Is the sum of angles ABC and CDA is [#permalink]

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24 Mar 2008, 08:13
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ABCD is a quadrilateral. Is the sum of angles ABC and CDA is equal to the sum of angles BCD and DAB?

(1) Circle O is inscribed in ABCD.

(2) Circle O is circumscribed about ABCD.

Please explain your answer. I thought this question was straight forward, but apparently I got tricked.
cheers

Kudos [?]: 1077 [0], given: 1

CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4724 [1], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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24 Mar 2008, 09:12
1
KUDOS
Expert's post
B

For a square the sum of angles ABC and CDA is equal to the sum of angles BCD and DAB under both conditions.

1. we can construct a rhombus (see a drawing) in which the sums will not be equal. insufficient
2. for any quadrilateral inscribed in a circle, the sums will always be equal (see the drawing). sufficient
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Kudos [?]: 4724 [1], given: 360

SVP
Joined: 21 Jul 2006
Posts: 1509

Kudos [?]: 1077 [0], given: 1

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24 Mar 2008, 09:35
dude, you're just insane! hehe...the OA is B. Is there any quant problem that you just can't answer?? there has to be one...lol...thanks anyway...

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CEO
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24 Mar 2008, 09:36
what is the difference between inscribed and circumscribed?
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You tried your best and you failed miserably. The lesson is 'never try'. -Homer Simpson

Kudos [?]: 1091 [0], given: 4

CEO
Joined: 17 Nov 2007
Posts: 3583

Kudos [?]: 4724 [0], given: 360

Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40

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24 Mar 2008, 10:48
bmwhype2 wrote:
what is the difference between inscribed and circumscribed?

http://en.wikipedia.org/wiki/Inscribe
http://en.wikipedia.org/wiki/Circumscribe

BTW. Thanks, I corrected my typo...
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Kudos [?]: 4724 [0], given: 360

Re: DS: Quadrilateral   [#permalink] 24 Mar 2008, 10:48
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# ABCD is a quadrilateral. Is the sum of angles ABC and CDA is

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