Question

the angles of a triangle are in the ratio 2:3:4 . Find the difference between larger angle to smaller ?​

Answer 1

Answer:

40

Step-by-step explanation:

Let common multiple be x

Angles are 2x , 3x and 4x

2x + 3x + 4x = 180.....Angle sum property

9x = 180

x = 20

Largest angle = 4x = 80

Smallest angle = 2x = 40

Difference = 80 - 40 = 40

Answer 2

Answer:

Step-by-step explanation:

Let’s assume a triangle ABC with angles, <A, <B and <C.

Given, <A : <B : <C is equal to 2:3:4, let’s assume the values of angles as,

<A = 2x

<B = 3x

<C = 4x,

x is a whole number. You can see that we have taken the values of angles such that they are still in the ratio 2:3:4.

Now, we know that the sum of all the angles of a triangle is 180°.

So, in triangle ABC

<A + <B + <C = 180°

Putting values of angles,

2x + 3x + 4x = 180°

9x = 180°

x = 180°/9

x = 20°

So, angles are as follows,

<A = 2(x) = 2(20°) = 40°

<B = 3(x) = 3(20°) = 60°

<C = 4(x) = 4(20°) = 80°Let’s assume a triangle ABC with angles, <A, <B and <C.

Given, <A : <B : <C is equal to 2:3:4, let’s assume the values of angles as,

<A = 2x

<B = 3x

<C = 4x,

x is a whole number. You can see that we have taken the values of angles such that they are still in the ratio 2:3:4.

Now, we know that the sum of all the angles of a triangle is 180°.

So, in triangle ABC

<A + <B + <C = 180°

Putting values of angles,

2x + 3x + 4x = 180°

9x = 180°

x = 180°/9

x = 20°

So, angles are as follows,

<A = 2(x) = 2(20°) = 40°

<B = 3(x) = 3(20°) = 60°

<C = 4(x) = 4(20°) = 80°

then the diffrence is 40°