Question

) Three angles of a triangle are in the ratio of 3:4:2. Find the measure of each ​

Answer 1

according to the angle sum property:

3x + 4x + 2x = 180 degrees

9x = 180

x = 20 degrees

3x = 60 degrees

4x = 80 degrees

2x = 40 degrees

Answer 2

Given :-

Ratio of three angles = 3 : 4 : 2

To Find :-

The measure of the first angle.

The measure of the second angle.

The measure of the third angle.

Analysis :-

Consider the common ratio as a variable.

Multiply the variable to the sides.

According to the question, make an equation to find the value of the variable.

Substitute the value of the variable in the sides and get the angles.

Solution :-

Consider the common ratio as 'x'. Then the angles would be 3x, 4x and 2x.

We know that,

Sum of a triangle = 180°

Making an equation,

$\sf 3x+4x+2x=180$

$\sf 9x=180$

Finding the value of x,

$\sf x=\dfrac{180}{9}$

$\sf x=20$

Thus, the value of x is 20.

Substituting to get the angles,

First angle = 3x

= 3 × 20 = 60°

Second angle = 4x

= 4 × 20 = 80°

Third angle = 2x

= 2 × 20 = 40°

Therefore, the angles are 60°, 80° and 40° respectively.