Question

The angle of a triangle are in the ratio 2:3:4. Find the measure of each angel of the triangle​

Answer 1

Question :-

• The angle of a triangle are in the ratio 2:3:4. Find the measure of each angle of the triangle.

Answer :-

• The angles of the triangle are 40° , 60° and 80°.

Given :-

• The ratio of the angles of a triangle is 2 : 3 : 4

To find :-

• The measure of each angle.

Step by step explanation :-

It is given that, The ratio of angles of the triangle are 2 : 3 :4. We have to find the value of each angle.

Now, Let us take each angle as 2x , 3x and 4x.

We know that, Sum of all angles of a triangle is equal to 180 degrees.

So, If we add all these angles we'll get 180°.

Therefore, The equation will be :-

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

Adding 2x , 3x and 4x,

$\sf 9x = 180 \degree$

Transposing 9 from LHS to RHS, Changing the sign from (÷) to (×) :-

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

Now, Dividing 180 by 9 :-

$\sf x =20 \degree$

Hence, x = 20°.

Thus, The angles of the triangle are :-

$\sf 2x = 2 \times 20 \degree = 40 \degree$

$\sf 3x = 3 \times 20 \degree = 60 \degree$

$\sf 4x = 4 \times 20 \degree = 80 \degree$

Therefore, The angles are 40° , 60° and 80°.