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

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

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New post 28 Feb 2019, 00:09
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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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Re: The ratio of the degree measures of the angles of a triangle is 2 : 3  [#permalink]

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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]

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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]

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New post 11 Mar 2019, 22:44

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]

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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]

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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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