Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD

Okay so I made an educated guess and got this question right- but kudos for feedback in my reasoning because I don't want to choke or second guess myself on test day.



Line DB divides Rectangle ABCD into two equal triangles. Is Angle ABD equal to 30 degrees.

(1) One side of Triangle ABD is equal to 2.

(2) One side of Rectangle ABCD is 1.


Statement (1) tells us that one side of triangle ABD is equal to 2- well, which side is that? Is it the side that corresponds to one of the two 90 degree angles in the rectangle. Also, we cannot just assume that the two triangles are 45 45 for the sake of not falling into GMAT DS traps. If that were true then, that is if mathematically the question and diagram in itself validated a 45 45 90 triangle, then the purpose of the question is defeated- in other words, the whole point of this question is to establish whether or not we have enough information to conclude angle ABD is equal to 30; therefore, nothing in the question or diagram itself can solve that question. The information needed to solve the question, or lack of it, is derived from the two statements.


Statement (2) tells us one side of the rectangle is 1- which side is that though? And how can we compute the length of the other side with this data. If we could do that then maybe we could extrapolate ratios through degrees based on the side lengths but the side lengths have no limitation (etc. you could have two sides of 1 and two sides of 3, or two sides of 1 and two sides of 2). Hence, this statement is insufficient.


If we combine both of these statements, we still do not have enough information- we cannot just use the Pythagorean theorem to find the hypotenuse length and derive a conclusion about the angles of the triangle by squaring 1 and 2. This is my best guest/ reasoning.