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In △ABC, is any angle greater than 90°?

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In △ABC, is any angle greater than 90°?  [#permalink]

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New post Updated on: 22 Oct 2018, 07:59
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In △ABC, is any angle greater than 90°?

(1) AB = 2, BC = 8, AC = 9
(2) Sum of the greatest and the second greatest angle is 160°

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A Kudos is one more question and its answer understood by somebody !!!

Originally posted by adstudy on 18 Jul 2018, 00:06.
Last edited by gmatbusters on 22 Oct 2018, 07:59, edited 1 time in total.
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Re: In △ABC, is any angle greater than 90°?  [#permalink]

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New post 18 Jul 2018, 00:15
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adstudy wrote:
In △ABC, is any angle greater than 90°?

(1) AB = 1, BC = 8, AC = 9
(2) Sum of the greatest and the second greatest angle is 160°


If we have the lengths of sides of a triangle, then to determine whether the triangle is acute (all angles less than 90) or right angled (one angle = 90) or obtuse (one angle > 90); we should square all the three lengths of sides.
If square of longest side is smaller than the sum of squares of two smaller sides, its an acute angled triangle
If square of longest side is equal to the sum of squares of two smaller sides, its a right angled triangle
If square of longest side is greater than the sum of squares of two smaller sides, its an obtuse angled triangle

(1) As the lengths are given, we can square and determine the answer. Sufficient (Its obtuse by the way, so one angle will be > 90).

(2) If sum of two angles = 160, both could be less than 90 (80, 80) or one could be greater than 90 (100, 60). Not sufficient.

Hence A answer
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Re: In △ABC, is any angle greater than 90°?  [#permalink]

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New post 18 Jul 2018, 00:41
1) As length of all three sides are given, a unique triangle can be constructed and hence angles can be determined.
SUFFICIENT.

2) sum of largest and second largest angle = 160.
Now the 2 angles can be 100, 60 or 80,80.
Hence NOT SUFFICIENT.

Answer A

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Re: In △ABC, is any angle greater than 90°?  [#permalink]

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New post 22 Oct 2018, 07:43
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I think the answer is E since "Given a triangle ABC, the sum of the lengths of any two sides of the triangle is greater than the length of the third side". In this way, in statement (1), AB+BC=1+8=9=AC, thus such triangle does not exist. In this way, statement (1) is wrong as well.

amanvermagmat wrote:
adstudy wrote:
In △ABC, is any angle greater than 90°?

(1) AB = 1, BC = 8, AC = 9
(2) Sum of the greatest and the second greatest angle is 160°


If we have the lengths of sides of a triangle, then to determine whether the triangle is acute (all angles less than 90) or right angled (one angle = 90) or obtuse (one angle > 90); we should square all the three lengths of sides.
If square of longest side is smaller than the sum of squares of two smaller sides, its an acute angled triangle
If square of longest side is equal to the sum of squares of two smaller sides, its a right angled triangle
If square of longest side is greater than the sum of squares of two smaller sides, its an obtuse angled triangle

(1) As the lengths are given, we can square and determine the answer. Sufficient (Its obtuse by the way, so one angle will be > 90).

(2) If sum of two angles = 160, both could be less than 90 (80, 80) or one could be greater than 90 (100, 60). Not sufficient.

Hence A answer
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Re: In △ABC, is any angle greater than 90°?  [#permalink]

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New post 22 Oct 2018, 08:02
Hi
There was a typo in the statement 1, It is revised now.
Thanks for reporting.

kaylajiang wrote:
I think the answer is E since "Given a triangle ABC, the sum of the lengths of any two sides of the triangle is greater than the length of the third side". In this way, in statement (1), AB+BC=1+8=9=AC, thus such triangle does not exist. In this way, statement (1) is wrong as well.

amanvermagmat wrote:
adstudy wrote:
In △ABC, is any angle greater than 90°?

(1) AB = 2, BC = 8, AC = 9
(2) Sum of the greatest and the second greatest angle is 160°


If we have the lengths of sides of a triangle, then to determine whether the triangle is acute (all angles less than 90) or right angled (one angle = 90) or obtuse (one angle > 90); we should square all the three lengths of sides.
If square of longest side is smaller than the sum of squares of two smaller sides, its an acute angled triangle
If square of longest side is equal to the sum of squares of two smaller sides, its a right angled triangle
If square of longest side is greater than the sum of squares of two smaller sides, its an obtuse angled triangle

(1) As the lengths are given, we can square and determine the answer. Sufficient (Its obtuse by the way, so one angle will be > 90).

(2) If sum of two angles = 160, both could be less than 90 (80, 80) or one could be greater than 90 (100, 60). Not sufficient.

Hence A answer

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In △ABC, is any angle greater than 90°?  [#permalink]

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New post 22 Oct 2018, 12:28
amanvermagmat wrote:
adstudy wrote:
In △ABC, is any angle greater than 90°?

(1) AB = 2, BC = 8, AC = 9
(2) Sum of the greatest and the second greatest angle is 160°


If we have the lengths of sides of a triangle, then to determine whether the triangle is acute (all angles less than 90) or right angled (one angle = 90) or obtuse (one angle > 90); we should square all the three lengths of sides.
If square of longest side is smaller than the sum of squares of two smaller sides, its an acute angled triangle
If square of longest side is equal to the sum of squares of two smaller sides, its a right angled triangle
If square of longest side is greater than the sum of squares of two smaller sides, its an obtuse angled triangle

(1) As the lengths are given, we can square and determine the answer. Sufficient (Its obtuse by the way, so one angle will be > 90).

(2) If sum of two angles = 160, both could be less than 90 (80, 80) or one could be greater than 90 (100, 60). Not sufficient.

Hence A answer


Hi amanvermagmat ,

Congrats (and kudos)!

Your solution (with very well-written details included) was really a pleasure to read!

Important (for all readers): we must consider 2 in the place of 1, as I have shown in bold red. Otherwise the triangle does not exist!
(This detail was correctly pointed out by kaylajiang . Kudos, too!)

Regards,
Fabio.
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In △ABC, is any angle greater than 90°?   [#permalink] 22 Oct 2018, 12:28
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