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

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Bunuel
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The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   03 Jun 2018, 12:27
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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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D
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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   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] New post   03 Jun 2018, 13:32
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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
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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   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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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   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] New post   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.
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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   13 Nov 2018, 12:29
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Hi All,

We're told that the ratio of the degree measures of the angles of a triangle is 2:3:4. We're asked which of the following is the sum of the degree measures of the SMALLEST and LARGEST angles.

Since the ratio of the angles is 2:3:4, we can refer to those 3 angles as 2X, 3X and 4X, respectively. A triangle has 180 total degrees and those 3 angles would sum to 9X, meaning that 9X = 180.

9X = 180
X = 20

The 3 angles would be 40, 60 and 80. The sum of the smallest and largest angles would be 40+80 = 120.

Final Answer:
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D


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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   27 Jan 2019, 20:36
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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°


We can create the equation:

2x + 3x + 4x = 180

9x = 180

x = 20

The smallest angle is 2x = 40, and the largest angle is 4x = 80. Thus, their sum is 40 + 80 = 120.

Answer: D
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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   28 Feb 2019, 01:23
2x + 3x + 4x = 180
9x = 180
x = \(\frac{180}{9}\)
x= 20

2x = 2 x 20 =40
3x = 3 x 20 = 60
4x = 4 x 20 = 80

Sum of the degree measure of the smallest & the largest angle = 40 + 80 =120

IMO D
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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   11 Mar 2019, 14:12
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°


smallest angle: \(180°*\frac{2}{9}\)
largest angle: \(180°*\frac{4}{9}\)

Sum of smallest and largest angle:
\(180°(\frac{2}{9}+\frac{4}{9})=180°(\frac{2}{3})=60°*2=120°\)

Answer (D)
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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   11 Mar 2019, 22:44
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Solution


Given:
    • The ratio of the degree measures of the angles of a triangle is 2: 3: 4.

To find:
    • The sum of the degree measures of the smallest and largest angles.

Approach and Working:
If we assume the angles as 2k, 3k and 4k, then
    • Sum of smallest and largest angles = 2k + 4k = 6k, which is a multiple of 6.
    • Among the given choices, only one option is a multiple of 6 (which is 120°)

Hence, the correct answer is option D.

Answer: D

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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   11 Mar 2019, 23:21
Ratio= 2:3:4. So I can say that the angles are 2x,3x and 4x where x is variable. Also, sum of angles of a triangle is 180. So 2x+3x+4x = 9x = 180. So x = 20. This the angles are 2x = 40, 3x = 60, 4x = 80. So answer = 120 = D.

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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink] New post   12 Mar 2019, 23:17
2+3+4=9.
180÷9*2+4=120

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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3 [#permalink]
12 Mar 2019, 23:17
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