If triangle ABC is an isosceles triangle, what is ∠ABC?

[BTGmoderatorDC]

If triangle ABC is an isosceles triangle, what is ∠ABC?

(1) ∠CAB = 45 degrees
(2) ∠BCA = 90 degrees


OA B

Source: Magoosh

[Brent@GMATPrepNow]

If triangle ABC is an isosceles triangle, what is ∠ABC?

(1) ∠CAB = 45 degrees
(2) ∠BCA = 90 degrees

Target question: What is ∠ABC?

Given: Triangle ABC is an isosceles triangle
So, ∆ABC has 2 equal angles

Statement 1: ∠CAB = 45 degrees
Since ∆ABC has 2 equal angles, there are two possible triangles that satisfy statement 1:
Case a: ∠CAB = 45, ∠BCA = 45 and ∠ABC = 90. In this case, the answer to the target question is ∠ABC = 90 degrees
Case b: ∠CAB = 45, ∠BCA = 90 and ∠ABC = 45. In this case, the answer to the target question is ∠ABC = 45 degrees
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: ∠BCA = 90 degrees
This statement is much different.
We know that ∆ABC has 2 equal angles, but we also know that the 2 equal angles cannot both be 90 degrees, since all 3 angles must add to 180.
So, if the 2 equal angles were 90 degrees each, the third angle would have to be 0 degrees, which is impossible.
Since the 2 equal angles cannot both be 90 degrees, it must be the case that the OTHER 2 angles are the equal angles.
In other words, ∠BCA = 90, ∠CAB = 45 and ∠ABC = 45. So, the answer to the target question is ∠ABC = 45 degrees
Since we can answer the target question with certainty, statement 2 is SUFFICIENT

Answer: B

Cheers,
Brent