Question

if the angles of the triangle are in the ratio 2:3:4, what is the difference between greatest and smallest angles ​

Answer 1

Answer:

2x+3x+4x=180

9x=180

x=180/9

x=20

2x=40

4x=80

80-40=40

Answer 2

Question :

if the angles of the triangle are in the ratio 2:3:4, what is the difference between greatest and smallest angles .

Answer :

$\sf\blue{Given}$

• Ratio of angles is 2:3:4

$\sf\blue{to\:find}$

• difference between greatest and smallest angle

Explanation :

• let measure of first angle be 2x

• let measure of second angle be 3x

• let measure of third angle be 4x

Rule :

Sum of all angles of the triangle is 180°

$\longrightarrow\sf{2x + 3x + 4x = 180}$

$\longrightarrow\sf{5x + 4x = 180}$

$\longrightarrow\sf{9x = 180}$

$\longrightarrow\sf{x = \dfrac{180}{9}}$

$\longrightarrow\sf{x = 20 }$

• Smallest angle = 2x

$\longrightarrow\sf{2\times 20 }$

$\longrightarrow\sf\pink{40 }$

• Greatest angle = 4x

$\longrightarrow\sf{4\times 20 }$

$\longrightarrow\sf\pink{80 }$

$\bf\purple{Difference = 80 - 40}$

$\longrightarrow\sf\pink{40}$