Triangle Iso

[karthikpandian19]

[pemdas]

see draw

[anandhimanshu85]

IMO A

see draw

[LalaB]

one more approach -
remember-the measure of an exterior angle equals the sum of its two non-adjacent interior angles
below (<) means angle

so,<BAD+<ABD=<BDC or x+<ABD=2x => <ABD=x
so, we the triangle ABD is isosceles. from the q. stem we can see, that the triangle BDC is also isosceles

so, from the stmnt 1 -AD=6 ,so AD=BD=BC=6

stmnt 2 is insuff,since there is no info about any side of the triangles

[GMATGuruNY]

What is the length of side BC?

1. AD = 6
2. x = 36

To determine how the angles affect each other, PLUG IN.
Just be sure to:

-- Satisfy the conditions given in the problem.
-- Satisfy the rules of geometry (the sum of the angles inside a triangle must be 180, etc.).

The result is the following:



The values in the figure above show that ∠ABD = ∠DAB.
Thus, AD = BD = BC.

Question rephrased: What is the length of AD or BD?

Statement 1: AD = 6
SUFFICIENT.

Statement 2: x=36
No information about any of the lengths.
INSUFFICIENT.

The correct answer is A.

[RuiCunha]

what i dont get in this is why BAD = DBA, or as someone mencioned why BAD = x !

[ArunangsuSahu]

External angle = Sum of 2 opposite Internal angles

(A) is sufficient