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If triangle ABC is an isosceles triangle
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05 Nov 2012, 11:37

2

2

00:00

A

B

C

D

E

Difficulty:

25% (medium)

Question Stats:

70% (00:58) correct 30% (00:53) wrong based on 295 sessions

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

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

For a detailed discussion of that most amazing geometric theorem, the Isosceles Triangle Theorem, as well as a video explanation of this particular question, see this this link: http://magoosh.com/gmat/2012/isosceles- ... -the-gmat/

Re: If triangle ABC is an isosceles triangle
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25 Sep 2013, 00:06

1

kanusha wrote:

sir, pls any explain why statement A wrong and statement B is rght......

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

(1) ∠CAB = 45 degrees. The sum of the remaining two angles is 180-45=135 degrees. Triangle ABC can be 45-45-90 right isosceles triangle OR 67.5-67.5-45 isosceles triangle. Angle B can be 45, 90, or 67.5 degrees. Not sufficient.

(2) ∠BCA = 90 degrees. This statement says that we have 45-45-90 isosceles right triangle, where C=90 degrees, therefore the remaining two angles must be 45 degrees each. Sufficient.

If triangle ABC is an isosceles triangle
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06 Mar 2018, 00:29

As we know by the properties of Isosceles , 90-45-45 , From A : we know about angle CAB is 45 , but we do not have an information about the other angles if any of them has a 90 degree measure. Other angles can be anything to form 180 degree From B : We know Angle BCA has a measure of 90 degree , Hence we can derive a conclusion that it follows an essential Isosceles pattern of 90 degree . other two sides must be 45 deg & 45 deg .

I'm sure there will be better explanations than this , but I chose B from this logic.
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Re: If triangle ABC is an isosceles triangle
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07 Mar 2018, 02:36

Bunuel wrote:

kanusha wrote:

sir, pls any explain why statement A wrong and statement B is rght......

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

(1) ∠CAB = 45 degrees. The sum of the remaining two angles is 180-45=135 degrees. Triangle ABC can be 45-45-90 right isosceles triangle OR 67.5-67.5-45 isosceles triangle. Angle B can be 45, 90, or 67.5 degrees. Not sufficient.

(2) ∠BCA = 90 degrees. This statement says that we have 45-45-90 isosceles right triangle, where C=90 degrees, therefore the remaining two angles must be 45 degrees each. Sufficient.

Re: If triangle ABC is an isosceles triangle
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07 Mar 2018, 02:42

shringi87 wrote:

Bunuel wrote:

kanusha wrote:

sir, pls any explain why statement A wrong and statement B is rght......

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

(1) ∠CAB = 45 degrees. The sum of the remaining two angles is 180-45=135 degrees. Triangle ABC can be 45-45-90 right isosceles triangle OR 67.5-67.5-45 isosceles triangle. Angle B can be 45, 90, or 67.5 degrees. Not sufficient.

(2) ∠BCA = 90 degrees. This statement says that we have 45-45-90 isosceles right triangle, where C=90 degrees, therefore the remaining two angles must be 45 degrees each. Sufficient.

Answer: B.

Hope it's clear.

Still cant understand why A cannot be an answer

The first statement in no sufficient because from (1) we could have more than one value of ∠ABC.
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Re: If triangle ABC is an isosceles triangle
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07 Jan 2019, 07:36

Top Contributor

mikemcgarry wrote:

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

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Re: If triangle ABC is an isosceles triangle
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07 Jan 2019, 07:36