In quadrilateral ABCD, is angle D ≤ 100 degrees?

Question

quadrilateral ABCD.png In quadrilateral ABCD, is angle D ≤ 100 degrees? Statement #1 : AB = BC Statement #2 : angle A = angle B = angle C For a collection of 10 DS problems on geometry, including this one, as well as the OE for this particular question, see: GMAT Data Sufficiency Geometry Practice Question Mike :-)

nipunjain14 · Answer

St :1 AB= BC
no information on any of other two unknown angles , thus insufficient

St : 2 angle A=angle B = angle C

suppose angle A = 10
thus angle D will be - 330
if angle A = 100 then angle D = 60

Insufficient

St1+St2
Still not enough information to get exact values of the angle D
Insufficient.

Ans E

gauravraos · Answer

HI Bunuel can you please help me solve this question?

how can a angle in a quadilateral be 330 according to the above explanation. Bunuel

mikemcgarry · Answer

Dear gauravraos , I'm happy to respond. :-)

I hope you don't mind that I am answering rather than the super-genius Bunuel . A quadrilateral with one 330 degree angle and three 10 degree angles would look like this: quadrilateral with 330 degree angle.png This kind of quadrilateral is sometimes called a "dart." It's a concave quadrilateral, unlike most of the quadrilaterals you will meet on the GMAT. Does this make sense? Mike :-)

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In quadrilateral ABCD, is angle D ≤ 100 degrees?

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