Question

Q9
The angles of a triangle are in the ratio 2:3 : 4. The largest angle of the
triangle is
(a) 120°
(b) 100°
(c) 80°
(d) 60°​

Answer 1

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

then,

$= > 2x + 3x + 4x = 180 \\ = > 9x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 180 \\ = > x \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 20$

the largest angle is 4x = 4 x 20 = 80°

Answer 2

AnswEr :

• The largest angle of the triangle is 80° (option C) .

⠀━━━━━━━━━━━━━

GiveN :

• Angles of the triangle are in the ratio 2 : 3 : 4

To FinD :

• Largest angle of the triangle = ?

SoluTion :

Let's assume the values of angles as,

• ∠A = 2x

• ∠B = 3x

• ∠C = 4x

⠀━━━━━━━━━━━━━

Now, We know that the sum of all the angles of a triangle is 180°(Angle sum property).

So, in any ΔABC

∠A + ∠B + ∠C = 180°

Substituting the values as per our assumption,

➠ 2x + 3x + 4x = 180°

➠ 9x = 180°

➠ x = 180°/9

➠ x = 20°

⠀━━━━━━━━━━━━━

★ So, the angles are :

• ∠A = 2x = 2(20) = 40°

• ∠B = 3x = 3(20) = 60°

• ∠C = 4x = 4(20) = 80°

$\therefore$ The largest angle is 80°.

⠀━━━━━━━━━━━━━