If the angles of a triangle are in the ratio of 4 : 3 : 2, then the triangle

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Q: 141 (IAS/1999)
If the angles of a triangle are in the ratio of 4 : 3 : 2, then the triangle

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,11,17,3,6,8,11

keywords: 

{'angles': [0, 1, 1, 0], 'triangle': [0, 1, 0, 1], 'angle': [0, 0, 1, 0], 'right triangle': [0, 1, 0, 0], 'ratio': [1, 0, 1, 12]}

To determine the nature of the triangle based on the given ratio of angles, we need to consider the sum of the angles in a triangle, which is always 180 degrees.

Let`s denote the angles of the triangle as 4x, 3x, and 2x, where x is a constant.

According to the given ratio, we have:

4x + 3x + 2x = 180

Simplifying the equation, we get:

9x = 180

Dividing both sides by 9, we find:

x = 20

Now, we can substitute the value of x back into the angles:

Angle 1 = 4x = 4 * 20 = 80 degrees

Angle 2 = 3x = 3 * 20 = 60 degrees

Angle 3 = 2x = 2 * 20 = 40 degrees

Based on these angles, we can conclude that the triangle is acute, meaning all angles are less than 90 degrees. Therefore, the correct option is "is acute."