Question

If the angles of a triangle are in the ratio 2:3:4,then find the difference between the greatest and smallest angles.​

Answer 1

Answer:

The Difference between the largest angle and smallest angle is 40°.

Step-by-step explanation:

Given :

Ratio of the angles = 2:3:4

To find :

The difference between the smallest and largest angle.

Solution :

Let the angles be -

• 2x
• 3x
• 4x

According to the angle sum property of triangle, sum of all angles in a triangle is 180°.

$\tt{\leadsto} \: 2x + 3x + 4x = 180 \\ \\ \tt{\leadsto} \: 9x = 180 \\ \\ \tt{\leadsto} \: x = \dfrac{180}{9} \\ \\ \tt{\leadsto} \: x = 20$

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Angles - }}}$

★ Value of 2x

$\tt{\leadsto} \: 2(20) \\ \\ \tt{\leadsto} \: 40$

One angles = 40°

$\rule{300}{0.5}$

★ Value of 3x

$\tt{\leadsto} \: 3(20) \\ \\ \tt{\leadsto} \: 60$

Second angle = 60°

$\rule{300}{0.5}$

★ Value of 4x

$\tt{\leadsto} \: 4(20) \\ \\ \tt{\leadsto} \: 80$

Third angle = 80°

$\rule{300}{1.5}$

✯ $\textsf{\underline{\underline{Difference - }}}$

Smallest angle = 40°

Largest angle = 80°

Their difference =

$\tt{\leadsto} \: 80 - 40 \\ \\ \tt{\leadsto} \: 40$

Difference = 40°

$\therefore$ The Difference between the largest angle and smallest angle is 40°.

Answer 2

Answer:

40°

Step-by-step explanation:

2 : 3 : 4 is the ratio of the angles.

Find the difference of smallest and the largwst angle.

Let the angles be 2x , 3x and 4x as per the ration given.

Using Angle Sum Property

= 2x + 3x + 4x = 180°

= 9x = 180°

= x = 180 / 9

Value of x = 20

1. Value of the angle 2x
2. Value of the angle 2xValue of the angle 3x
3. Value of the angle 2xValue of the angle 3xValue of the angle 4x

1. 2x = 2 (20) = 40°
2. 3x = 3 (20) = 60°
3. 4x = 4 (20) = 80°

Now, this angles are 40 , 60 and 80 as per the question the difference between smallest and greatest angles = ( 40 and 80 ) subtracting the greatest angle and the smallest angle we get the answer.

40° - 80° = 40°

Hence, the difference between the greatest and smallest angle is 40°