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
Source: Princeton Review
The ratio of the degree measures of the angles of a triangle
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let the degrees be 2x, 3x and 4x.
Sum of degrees = 9x
9x = 180 degrees, solving for x, x= 20 degrees
Thus, the smallest angle = 2x = 2x20= 40 degrees
The largest angle = 4x = 4x20 = 80 degrees
Sum of smallest and largest angles = 40+80 = 120 degrees
Sum of degrees = 9x
9x = 180 degrees, solving for x, x= 20 degrees
Thus, the smallest angle = 2x = 2x20= 40 degrees
The largest angle = 4x = 4x20 = 80 degrees
Sum of smallest and largest angles = 40+80 = 120 degrees
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BTGmoderatorDC 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°
OA D
Source: Princeton Review
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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