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M16-10

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Bunuel
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M16-10 [#permalink] New post   16 Sep 2014, 00:58
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A
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C
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Difficulty:

25% (medium)

Question Stats:

80% (01:50) correct 20% (01:30) wrong based on 40 sessions
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Is triangle \(ABC\) a right triangle?


(1) \(\angle ABC = \angle BCA\)

(2) \(\angle ABC = \angle CAB + 30\) degrees
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C
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Bunuel
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Re M16-10 [#permalink] New post   16 Sep 2014, 00:58
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Statement (1) by itself is insufficient. The triangle is isosceles but this imposes no restrictions on angle \(CAB\).

Statement (2) by itself is insufficient. Assigning different values to angle \(CAB\), we will get different triangles. If \(CAB = 60\) or \(30\), the triangle is a right triangle.

Statements (1) and (2) combined are sufficient. S1 and S2 provide a system of three linear equations (the third equation is derived from the condition that the sum of the angles equals 180 degrees) with three unknown variables. From this system, we can find the value of each angle.


Answer: C
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Re: M16-10 [#permalink] New post   13 Jul 2016, 11:15
Hello,

Can you please share how the property that all interior angles sum to 180 helps us get answer C. Thanks in advance for your help?
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Re: M16-10 [#permalink] New post   13 Jul 2016, 11:40
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abhilash53 wrote:
Hello,

Can you please share how the property that all interior angles sum to 180 helps us get answer C. Thanks in advance for your help?


We'll have x + x + (x - 30) = 180 --> x = 70. So, the angles are 70, 70 and 40.
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Re: M16-10 [#permalink] New post   22 Mar 2017, 22:10
Since from (1) and (2) we have:
(1) B = C
(2) A+30 = B or A =B-30
and A+B+C = 180,
(B-30)+B+B = 180
3B = 210
B = 70

Since B=70, C=70, and A=40
(1)+(2) Sufficient. C.
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Re: M16-10 [#permalink] New post   30 May 2017, 07:14
Question becomes much easier once you have drawn the figure.

Angle ABC, CAB and BCA can become confusing without the figure.
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Re: M16-10 [#permalink] New post   15 Jan 2021, 11:14
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Re: M16-10 [#permalink]
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