Question

Q:- 19- The angles of a triangle are in the
ratio 2:3:4, then the measure of the
angles of the triangle are​

Answer 1

$\bf{\underline{Question:-}}$

The angles of a triangle are in the

ratio 2:3:4, then the measure of the

angles of the triangle are.

$\bf{\underline{Given:-}}$

• angles of a triangle are in the
• ratio 2:3:4

$\bf{\underline{To\:Find:-}}$

• Measure of all angle ?

$\bf{\boxed{\red{\underline{Identity \: of\: Triangle:-}}}}$

• Sum of Three angles of triangle is 180°

$\bf{\underline{Solution:-}}$

• Let the all angle's ratio be x

So,

$\sf :→ 2x + 3x +4x=180°$

$\sf :→ 5x + 4x = 180°$

$\sf :→ 9x=180°$

$\sf :→ x = 180/9$

$\sf :→ x = 20°$

$\bf{\underline{Substituting\:value\:of\:X\:in\:given\:ratio's:-}}$

• Measure of all angles
• First angle 2x = 2×20 = 40°
• Second angle 3x = 3×20 = 60°
• third angle 4x = 4×20 = 80°

$\bf{\underline{Verification:-}}$

• Sum of Three angles of triangle is 180°

→ ∠A + ∠B + ∠C = 180°

→ 40 + 60 + 80 = 180°

→ 100 + 80 = 180°

→ 180° = 180°

$\bf{\underline{Hence:-}}$

• Verified

Answer 2

Given ,

The angles of a triangle are in the ratio 2 : 3 : 4

Let ,

The angles of triangle are 2x , 3x and 4x

As we know that ,

The sum of all angles of triangle is 180

Thus ,

$\tt \implies 2x + 3x + 4x = 180</p><p></p><p>$

$\tt \implies 9x = 180</p><p>$

$\tt \implies x = \frac{180}{9}$

$\tt \implies x = 20$

The measure of the angles of the triangle are 40 , 60 and 80