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# The ratio of the degree measures of the angles of a triangle is 2 : 3

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Math Expert
Joined: 02 Sep 2009
Posts: 49320
The ratio of the degree measures of the angles of a triangle is 2 : 3  [#permalink]

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03 Jun 2018, 12:27
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Difficulty:

15% (low)

Question Stats:

85% (00:30) correct 15% (00:27) wrong based on 98 sessions

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The ratio of the degree measures of the angles of a triangle is 2:3:4. Which of the following is the sum of the degree measures of the smallest and largest angles?

A) 40°

B) 80°

C) 100°

D) 120°

E) 140°

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Posts: 859
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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3  [#permalink]

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03 Jun 2018, 13:11
Bunuel wrote:
The ratio of the degree measures of the angles of a triangle is 2:3:4. Which of the following is the sum of the degree measures of the smallest and largest angles?

A) 40°

B) 80°

C) 100°

D) 120°

E) 140°

Let the measure of angles of the triangle is 2k, 3k and 4k degrees where 2k and 4k are the the measure of smallest and largest angle respectively.

we have asked to find out the measure of 2k+4k=6k

Now we have 2k+3k+4k=180 deg
or, 9k=180
or, k=$$\frac{180}{9}$$=20 deg

So the desired measure=6k=6*20=120 deg.

Hence, the option (D) is the correct answer.
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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3  [#permalink]

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03 Jun 2018, 13:32
1
Bunuel wrote:
The ratio of the degree measures of the angles of a triangle is 2:3:4. Which of the following is the sum of the degree measures of the smallest and largest angles?

A) 40°

B) 80°

C) 100°

D) 120°

E) 140°

because ratio is 1:2,
sum must be a multiple of 3
only 120°
D
Intern
Joined: 26 Feb 2018
Posts: 19
Re: The ratio of the degree measures of the angles of a triangle is 2 : 3  [#permalink]

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05 Jun 2018, 08:37
Bunuel wrote:
The ratio of the degree measures of the angles of a triangle is 2:3:4. Which of the following is the sum of the degree measures of the smallest and largest angles?

A) 40°

B) 80°

C) 100°

D) 120°

E) 140°

Given ratio of angles of a triangle is 2:3:4, 2x + 3x + 4x = 180

9x = 180
x = 20

smallest = 2x = 2*20 = 40
largest = 4x = 4*20 = 80

40 + 80 = 120 ans D
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Posts: 382
Re: The ratio of the degree measures of the angles of a triangle is 2 : 3  [#permalink]

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05 Jun 2018, 11:53
Given ration 2:3:4 so angles can be considered 2x,3x,4x
2x+3x+4x=180
x=20

Smallest angle 40 and Largest Angle 80. Sum of Smallest and Largest angle is 120
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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3  [#permalink]

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10 Jun 2018, 15:54
Bunuel wrote:
The ratio of the degree measures of the angles of a triangle is 2:3:4. Which of the following is the sum of the degree measures of the smallest and largest angles?

A) 40°

B) 80°

C) 100°

D) 120°

E) 140°

As per the ratio, the smallest angle is 2x and largest angle is 4x. So the sum of this 2 angles is 6x. We can deduce that sum is basically multiple of 6.
Option D works.

Thus , option D is the answer.
Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 &nbs [#permalink] 10 Jun 2018, 15:54
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