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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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The ratio of the degree measures of the angles of a triangle
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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
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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deloitte247
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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
$$answer\ is\ option\ D$$
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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abhishekgoswami1234u
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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
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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Scott@TargetTestPrep
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We can create the equation:AAPL wrote:Princeton Review
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°
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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