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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

by BTGmoderatorDC » Sun Jul 14, 2019 2:39 am

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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

Source: Princeton Review
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by swerve » Mon Jul 15, 2019 10:10 am
Given ratio of angles of a triangle is \(2:3:4\), \(2x + 3x + 4x = 180\)

\(9x = 180\)
\(x = 20\)

smallest \(= 2x = 2\cdot 20 = 40\)
largest \(= 4x = 4\cdot 20 = 80\)

\(40 + 80 = 120^{o}\) ans __D__
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by Darkknightreturning » Sun Jul 21, 2019 2:47 am
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
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by Scott@TargetTestPrep » Tue Jul 30, 2019 8:39 am
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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