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If the angles of a triangle are in the ratio 2:3:7, the triangle is

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If the angles of a triangle are in the ratio 2:3:7, the triangle is [#permalink]

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New post 08 Mar 2018, 02:14
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Difficulty:

  25% (medium)

Question Stats:

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If the angles of a triangle are in the ratio 2:3:7, the triangle is

(A) acute

(B) isosceles

(C) obtuse

(D) right

(E) equilateral
Spoiler: OA

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Re: If the angles of a triangle are in the ratio 2:3:7, the triangle is [#permalink]

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New post 08 Mar 2018, 02:15
Bunuel wrote:
If the angles of a triangle are in the ratio 2:3:7, the triangle is

(A) acute

(B) isosceles

(C) obtuse

(D) right

(E) equilateral


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Re: If the angles of a triangle are in the ratio 2:3:7, the triangle is [#permalink]

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New post 08 Mar 2018, 05:22
Bunuel wrote:
If the angles of a triangle are in the ratio 2:3:7, the triangle is

(A) acute

(B) isosceles

(C) obtuse

(D) right

(E) equilateral


Ratio of angles in a triangle = 2:3:7

i.e. Sum of the angles = 2x+3x+7x = 180
12x = 180

i.e. x = 15

i.e. angles are 2x = 30
3x = 45
7x = 105

i.e. one of the angles is Obtuse angle (Angles greater than 90º is called obtuse angle)

Hence

Answer: Option C
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Re: If the angles of a triangle are in the ratio 2:3:7, the triangle is [#permalink]

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New post 08 Mar 2018, 23:51
Bunuel wrote:
If the angles of a triangle are in the ratio 2:3:7, the triangle is

(A) acute

(B) isosceles

(C) obtuse

(D) right

(E) equilateral

IMO C
we know sum of interior angles of triangle= 180
now so each angle will be 2/2+3+7= 2/12 same with others
3/12 and 7/12
now divide 180*2/12=30
180*3/12=45
and 180*7/12=105
so if one angle is more then 90 then it is obtuse triangle
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Re: If the angles of a triangle are in the ratio 2:3:7, the triangle is [#permalink]

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New post 12 Mar 2018, 10:07
Bunuel wrote:
If the angles of a triangle are in the ratio 2:3:7, the triangle is

(A) acute

(B) isosceles

(C) obtuse

(D) right

(E) equilateral


We can create the equation:

2x + 3x + 7x = 180

12x = 180

x = 15

Our angles are 30, 45, and 105, so we have an obtuse triangle.

Answer: C
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Re: If the angles of a triangle are in the ratio 2:3:7, the triangle is [#permalink]

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New post 12 Mar 2018, 11:07
Bunuel wrote:
If the angles of a triangle are in the ratio 2:3:7, the triangle is

(A) acute

(B) isosceles

(C) obtuse

(D) right

(E) equilateral


The angles of the triangle are

1. \(\frac{2}{12}*180 = 30\)
2. \(\frac{3}{12}*180 = 45\)
3. \(\frac{7}{12}*180 = 105\)

Answer will be (C) obtuse angled triangle.
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Re: If the angles of a triangle are in the ratio 2:3:7, the triangle is [#permalink]

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New post 12 Mar 2018, 11:09
2+3+7=12x
12x = 180
X=15
7x =105. Obtuse


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Re: If the angles of a triangle are in the ratio 2:3:7, the triangle is   [#permalink] 12 Mar 2018, 11:09
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