Question

If the angles of a triangle abc are in the ratio 2:3:4, find the measures of the angles a,b,c.

Answer 1

Answer:

let the angle be 2x,3x,4x

we know that,

the sum of angle of triangle=180°

a/q,

2x+3x+4x=180°

9x=180°

x=20°

hence ,the angle are 40°,60,°,80°

Answer 2

Answer:

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

Step-by-step explanation:

Given :

Ratio of angles = 2 : 3 : 4

To find :

The measures of a triangle

Solution :

Let the angles be -

• $\angle$ a = 2y
• $\angle$ b = 3y
• $\angle$ c = 4y

According to the angle sum property of triangle, sum of all the angles is 180°. Following the same, the equation formed is -

$\sf{\longrightarrow} \: 2y + 3y + 4y = 180 \\ \\\sf{\longrightarrow} \: 5y + 4y = 180 \\ \\ \sf{\longrightarrow} \: 9y = 180 \\ \\ \sf{\longrightarrow} \: y = \dfrac{180}{9} \\ \\ \sf{\longrightarrow} \: y = 20$

$\rule{300}{1.5}$

★ Value of $\angle$ a -

$\sf{\longrightarrow} \: 2(20) \\ \\ \sf{\longrightarrow} \: 40^{\circ}$

$\rule{300}{1.5}$

★ Value of $\angle$ b -

$\sf{\longrightarrow} \: 3(20) \\ \\ \sf{\longrightarrow} \: 60^{\circ}$

$\rule{300}{1.5}$

★ Value of $\angle$ c -

$\sf{\longrightarrow} \: 4(20) \\ \\ \sf{\longrightarrow} \: 80^{\circ}$

$\therefore$ The angles of the triangle are 40°,60°, and 80°.