Question

if the angles of a triangle are in the ratio of 2:3:4 . find the value of each angle
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Answer 1

Answer:

Let 1st angle = 2x

Second angle =3x

Third angle=4x

Through the angle sum property of a triangle

→2x+3x+4x=180°

→9x=180°

→x = 180/9=20

Value of 1st angle = 2x= 2×20=40°

Second angle =3x=3×20=60°

Third angle=4x=4×20=80°

Answer 2

Given :

• Ratio of angle = 2 : 3 : 4

To find :

• Value of all angles

According to the question,

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

As we know,

Sum of all angles of a triangle = 180°

➞ 2x + 3x + 4x = 180°

➞ 9x = 180°

➞ x = 180° ÷ 9

➞ x = 20°

• So,the value of x is 20°.

★ Value of 2x :

➞ 2x

➞ 2(20°)

➞ 40°

★ Value of 3x :

➞ 3x

➞ 3(20°)

➞ 60°

★ Value of 4x :

➞ 4x

➞ 4(20°)

➞ 80°

• So, the value of all angles of a triangle is 40°,60° and 80°.

___________________

★ Verification :

Sum of all angles of a triangle = 180°

➞ 2x + 3x + 4x = 180°

➞ 9x = 180°

➞ 9(20°) = 180°

➞ 180° = 180°

.°. L.H.S = R.H.S

Hence,verified.