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This one is driving me nuts. It's from the OG Quantitative review and the explanation is very vague.

(note that the measure of angles BDC and BCD is 2x degrees)

In triangle ABC above, what is the length of side BC

(1) Line segment AD has length 6. (2) x =36

The answer should be "A".

angle DAB = angle DBA = x
this means, ABD is an isosceles triangle
=> AD = BD
but it's given in the figure that, BD = BC (BDC is also an isosceles triangle)

This one is driving me nuts. It's from the OG Quantitative review and the explanation is very vague.

(note that the measure of angles BDC and BCD is 2x degrees)

In triangle ABC above, what is the length of side BC

(1) Line segment AD has length 6. (2) x =36

The answer should be "A".

angle DAB = angle DBA = x this means, ABD is an isosceles triangle => AD = BD but it's given in the figure that, BD = BC (BDC is also an isosceles triangle)

=> AD=BD=BC=6

Is it clear?

For me it is not clear how do you assume that DAB = DBA.... It is actually the essiantial info in answering this question. I tried to prove it but didn't find the way.

One of the properties on the exterior angle of any triangle is:

in this case Angle BDC (exterior angle of triangle ADB) = Angle DAB +Angle DBA. Which translates to 2x = x+x. Hence Angle, DAB=Angle DBA. This is not an assumption. Since both the angles are x degrees, they are equal. Hence, AD=DB and we already know that BD =DC.

Gordon & Vivek, you are both right, the OA is A. However, you are both assuming the one part of the explanation that I dont understand. I understand the property that an exterior angle of a triangle is equal to the sum od the two remote interior angles so angle BDC = 2x, therefore, 2x = DAB + DBA. But how do we know they are both equal????

One of the properties on the exterior angle of any triangle is:

in this case Angle BDC (exterior angle of triangle ADB) = Angle DAB +Angle DBA. Which translates to 2x = x+x. Hence Angle, DAB=Angle DBA. This is not an assumption. Since both the angles are x degrees, they are equal. Hence, AD=DB and we already know that BD =DC.

I hope this is more clear Kook.

Gordon, this can't be assumed unless it is given. What if 2x = 0.5x+1.5x?

kook44,
Are we missing anything in the question itself?

Gordon, this can't be assumed unless it is given. What if 2x = 0.5x+1.5x?

kook44, Are we missing anything in the question itself?

I agree with you - that's why I can't see the solution. And no - the is nothing missing from the question (maybe there is a typo in the guide???). Its #117 in the OG Quantitative Review.

I really think there is a typo in the guide, and one of the angles BAD or ABD was intended to have been labeled explicitly as "x". Then it would all make sense.

the answer will be A ,, I got this prob on gmatprep test today .i marked E . post reading this post its clear to me that it is A :

now Angl A = X Angl BDC =2X Angl DCB =2X NOW WE KNOW 2X=X + Angl ABD => Angl ABD = 2X-X = X SO AD=BD STMT1 GVN AD=6 THEN BD=6 GVN BD=BC HENSE AD=BD=BC=6

Below is correct form of this question. Note that angle BAC equals to x degrees.

Attachment:

trig2uc8.png [ 9.64 KiB | Viewed 1883 times ]

In triangle ABC above, what is the length of side BC?

As <BDC=<BCD then the BD=BC. Also as <ADB=180-2x (exterior angle) and the sum of the angles of a triangle is 180 degrees then in triangle ADB we'll have: x+(180-2x)+<ABD=180 --> <ABD=x. Now, we have that <ABD=x=<DAB so AD=BD --> AD=BD=BC.

Question: BC=?

(1) Line segment AD has length 6 --> AD=BD=BC=6. Sufficient. (2) x = 36 --> we know only angles which is insufficient to get the length of any line segment.