Question

the ratio of the measures of the three angles of a triangle is 2 :3:4. the measure of the largest angle is​

Answer 1

Answer:-

Largest angle = 80°

Given:-

The ratio of the sides of the triangle is 2 : 3 : 4.

To find :-

The largest angle.

Solution :-

Let the angle in ratio be 2x , 3x and 4x

A/Q.

The sum of all angles of a triangle is 180°.

→ 2x + 3x + 4x = 180° (Angle sum property)

→9x = 180

→ x = 180/ 9

→ x = 20°

Put the value of x,

2x = 3 × 20 = 40°

3x = 3 × 20 = 60°

4x = 4 × 20 = 80°

hence, the largest angle is 80°.

Answer 2

Solution:-

=> The angels of triangle are in the ratio of 2 : 3 : 4

Now

=> Let the angle triangle are 2x , 3x , 4x

Using Angles sum property

=> Sum of all three angle of triangle is 180⁰

Applying this property

=> 2x + 3x + 4x = 180⁰

=> 5x + 4x = 180⁰

=> 9x = 180⁰

=> x = 180⁰/9

=> x = 20⁰

Now we get

=>∠1 = 2 × 20⁰ = 40⁰

=> ∠2 = 3 × 20⁰ = 60⁰

=> ∠3 = 4 × 20⁰ = 80⁰

We have to find

=> The largest angle is 80⁰

Answer

=> 80⁰