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The ratio of the degree measures of the angles of a triangle

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The ratio of the degree measures of the angles of a triangle

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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°

OA D.

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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: D

GMAT assassins aren't born, they're made,
Rich

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ratio of the degree of each angle in the triangle is 2, 3, 4 respectively
Total sum of of all interior angle of a a triangle = 180 degree
Let unknown angle = x
$$2x:3x:4x=180$$
$$2x+3x+4x=180$$
$$\frac{9x}{9}=\frac{180}{9}$$
$$x=20 degree$$
Hence the degree measures of angles are
$$2\left(20\right):3\left(20\right):4\left(20\right)$$
$$40:60:80$$
sum of the smallest and largest angle = 80 + 40 = 120 degree
$$answer\ is\ option\ D$$

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Answer: D
The sum of the angles in a triangle is equal to 180 degrees.
Since the angles are in the ration of 2:3:4, we can say that the angles are (2/9)*180, (3/9)*180, (4/9)*180, i.e 40,60,80 degrees.
So, the sum of the smallest and the largest angles are 40+80=120 degrees.
Hence the answer

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First add up all the ratios 2:3:4 = 9. Since a triangle has 180 degrees, that is a factor of 20.

Multiple the ratio to get 40:60:80, which adds up to 180.

Now add the smallest and largest angle, you get 120

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