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

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BTGmoderatorDC: Moderator; Posts: 7187; Joined: Thu Sep 07, 2017 4:43 pmFollowed by: 23 members

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

Source: Beat The GMAT — Problem Solving | Sun Jul 14, 2019 2:39 am

swerve: Legendary Member; Posts: 2604; Joined: Sun Oct 29, 2017 2:04 pmFollowed by: 6 members

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__

Darkknightreturning: Junior | Next Rank: 30 Posts; Posts: 21; Joined: Mon Jul 01, 2019 8:40 am

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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Scott@TargetTestPrep: GMAT Instructor; Posts: 8246; Joined: Sat Apr 25, 2015 10:56 amFollowed by: 29 members; Location: Los Angeles, CA; Thanked: 43 times

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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