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:

sum of three angles is 180

o

ratio of three angles are 2:3:4

First angle =2x

Second angle =3x

Third angle =4x

2x+3x+4x=180

9x=180

x=20

First angle =2(20)=40

o

Second angle =3(20)=60

o

Third angle =4(20)=80

o

Greatest angle =80

o

Answer 2

Answer :-

• The measure of the largest angle is 80°.

Given :-

• The ratio of the measures of the three angles of a triangle is 2 : 3 : 4.

To find :-

• The measure of the largest angle.

Step-by-step explanation :-

Detailed explanation of the solution :-

Let's understand!

As given in the question, the ratio of the measures of the three angles of a triangle is 2 : 3 : 4. We have to find the measure of the largest angle. To do this, first we have to find the measure of all the angles of the triangle, and then we will find out the largest angle using that.

Calculations :-

Since the measure of the three angles are in the ratio 2 : 3 : 4,

Therefore, let the angles be 2x, 3x and 4x.

We know that :-

Sum of all the angles in a triangle = 180°.

So, these angles must be equal to 180°.

Therefore, we get :-

$\sf2x + 3x + 4x = 180^{\circ}$

Adding 2x, 3x and 4x,

$\sf9x = 180^{\circ}$

Transposing 9 from LHS to RHS, changing it's sign,

$\sf x = \dfrac{180^{\circ}}{9}$

Dividing 180° by 9,

$\sf x = 20^{\circ}.$

The value of x = 20°.

Thus, the measure of all the angles are as follows :-

$\sf2x = 2 \times 20^{\circ} = 40^{\circ}$

$\sf3x = 3 \times 20^{\circ} = 60^{\circ}$

$\sf4x = 4 \times 20^{\circ} = 80^{\circ}$

The angles are 40°, 60° and 80° respectively.

It's clear that 80° is the largest angle here.

So, the measure of the largest angle = 80°.