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# Is ABC a right triangle?

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Manager
Joined: 27 Jul 2011
Posts: 53
Is ABC a right triangle?  [#permalink]

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24 Jun 2014, 07:59
1
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Difficulty:

45% (medium)

Question Stats:

59% (01:07) correct 41% (01:06) wrong based on 311 sessions

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Is ABC a right triangle?

(1) The angles of ABC are in the ratio 1 : 2 : 3.

(2) One of the angles of ABC equals the sum of the other two angles.
Math Expert
Joined: 02 Sep 2009
Posts: 55231
Re: Is ABC a right triangle?  [#permalink]

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24 Jun 2014, 08:09
1
Is ABC a right triangle?

(1) The angles of ABC are in the ratio 1 : 2 : 3. Since the sum of the angles in a triangle is 180°, then from this statement we have that x + 2x + 3x = 180. We can find all the angles, thus answer whether the triangle is right angled. Sufficient.

(2) One of the angles of ABC equals the sum of the other two angles. Say that angle is y°, then y + y = 180° --> y = 90°. Sufficient.

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Re: Is ABC a right triangle?  [#permalink]

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13 Dec 2016, 22:49
St1. 1+2+3=6, so we get 30:60:90. Suff

St2. x+y+(x+y)=180 => 2(x+y)=180=>x+y=90. Suff

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Re: Is ABC a right triangle?  [#permalink]

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03 Oct 2017, 23:02
smartyman wrote:
Is ABC a right triangle?

(1) The angles of ABC are in the ratio 1 : 2 : 3.

(2) One of the angles of ABC equals the sum of the other two angles.

Its a very simple question..
Given : a triangle ABC
DS: Is ABC a right triangle? i.e any one of the angle is 90` or not

Statement 1 : Lets say A:B:C :: 1:2:3 (we can assume any angles)
So, x+2x+3x = 180
6x = 180
x = 30
So, the angles are 30, 60, 90
ABC is a right angled triangle
SUFFICIENT

Statement 2: Lets say A= B+C (we can assume any angles)
Also A+B+C = 180
A+A = 180
A = 90
ABC is a right angles triangle
SUFFICIENT

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Re: Is ABC a right triangle?  [#permalink]

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26 Nov 2018, 00:03
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Re: Is ABC a right triangle?   [#permalink] 26 Nov 2018, 00:03
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