Question

In a triangle all the three angles are in the ratio 2:3:4.find the angles

Answer 1

AnsWer :

• 80, 60 , 40.

SolutioN :

• Let the sides of triangle be x.

All Sides of triangle become,

• 2x , 3x and 4x

Diagram :

$\setlength{\unitlength}{0.78 cm}\begin{picture}(12,4)\thicklines\put(5.4,5.8){ \tt{B} }\put(11.2,5.8){ \tt {C} }\put(8.4,10){ \tt{A} }\put(6,6){\line(2,3){2.5}}\put(11,6){\line(-2,3){2.5}}\put(6,6){\line(1,0){5}}\put(5,7.9){ \tt{2x} }\put(11,7.9){ \tt{3x} }\put(8,5){ \tt{4x} }\end{picture}$

We know that, Sum of all angles of triangle is 180°.

→ 2x + 3x + 4x = 180.

→ 9x = 180°.

→ x = 180/ 9.

→ x = 20°.

$\rule{90}2$

Now, Let's Find all sides.

• 2x.

→ 2x = 2 ( 20 ) = 40.

$\rule{90}2$

• 3x.

→ 3x = 3 ( 20 ) = 60.

$\rule{90}2$

• 4x.

→ 4x = 4 ( 20 ) = 80.

Therefore, the sides of triangle is 80 , 60 and 40.

Answer 2

${ \huge{ \bold{ \underline{ \underline{ \blue{Question:-}}}}}}$

In a triangle all the three angles are in the ratio 2:3:4.find the angles

_______________

${ \huge{ \bold{ \underline{ \underline{ \orange{Answer:-}}}}}}$

✒Given : -

⠀⠀⠀ → Three angles = 2:3:4

⠀⠀⠀

✒To Find : -

⠀⠀⠀ → All angles of triangle ..

✒Let ,

⠀⠀⠀ → Angle 1 = 2x

⠀⠀⠀ → Angle 2 = 3x

⠀⠀⠀ → Angle 3 = 4x

✒Now ,

${ \large{ \bold{ \underline{ \underline{ \purple{According\:to\:the\:Question:-}}}}}}$

⠀⠀⠀ → Sum of all angles of ⠀⠀⠀⠀⠀⠀triangle is 180° ..

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

$\dashrightarrow\sf{9x=180\degree}$

$\dashrightarrow\sf{x=\cancel\dfrac{180\degree}{9}}$

$\leadsto\sf{{ \large{ \boxed{ \bold{ \bold{ \red{x=120}}}}}}}$

→ Here , the value of x is 120 ..

✒Then ,

$\dashrightarrow\sf{Angle\:1=2(20)}$

$\dashrightarrow\sf{40\degree}$

$\dashrightarrow\sf{Angle\:2=3(20)}$

$\dashrightarrow\sf{60\degree}$

$\dashrightarrow\sf{Angle\:3=4(20)}$

$\dashrightarrow\sf{80\degree}$