Question

the angles of triangle are in ratio 2:3:4 find the measure of each angle of the triangle ​

Answer 1

$\underline{\bigstar{\sf\ Given:-}}$

• Angles of triangle are in the ratio 2 : 3 : 4

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$\underline{\bigstar{\sf\ To\:Find:-}}$

• Measure of each angle of the triangle.

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$\underline{\bigstar{\sf\ Solution:-}}$

Let the angles of triangle be 2x , 3x and 4x

⇒ 2x + 3x + 4x = 180°

[ Angle sum property]

⇒ 9x = 180°

⇒ x = 180 / 9

⇒x = 20

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• 1st angle = 2 × 20 = 40 °
• 2nd angle = 3 × 20 = 60 °
• 3rd angle = 4 × 20 = 80 °

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Answer 2

• The first angle of the triangle = 40°.
• The second angle of the triangle = 60°.
• The third angle of the triangle = 80°.

Given :–

• Ratio of the measure of the angles of a triangle = 2 : 3 : 4.

To Find :–

• The measure of each angles of the triangle.

Solution :–

Let,

The first angle be 2x.

The second angle be 3x.

The third angle be 4x.

We have to find the measure of each angles of the triangle.

We know that,

Sum of all the angles of the triangle = 180°

I.e.,

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

$\mapsto 5x + 4x = 180 \degree$

$\mapsto 9x = 180 \degree$

$\mapsto x = \cancel\dfrac{180 \degree}{9}$

$\mapsto x = \dfrac{20\degree}{1}$

$\mapsto x = 20 \degree$

So, the angles are :

First angle = 2x = 2 × 20° = 40°.

Second angle = 3x = 3 × 20° = 60°.

Third angle = 4x = 4 × 20° = 80°.

Hence,

The measure of each angles of the triangle is 40°, 60° and 80°.