If triangle ABC is an isosceles triangle, what is ∠ABC?
(1) ∠CAB = 45 degrees
(2) ∠BCA = 90 degrees
OA B
Source: Magoosh
If triangle ABC is an isosceles triangle, what is ∠ABC?
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Target question: What is ∠ABC?BTGmoderatorDC wrote:If triangle ABC is an isosceles triangle, what is ∠ABC?
(1) ∠CAB = 45 degrees
(2) ∠BCA = 90 degrees
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