Question

The three interior angle of a triangle are in the ratio 2 : 3 : 4. find the measure of the smallest angle of the triangle.​

Answer 1

Answer:

given :-

ratio of three angles of triangle are 2:3:4

let the common multiple be x.

so,

first angle =2x°

second angle =3x°

third angle=4x°

sum of all angles of triangle =180°

2x°+3x°+4x°=180°

9x°=180°

x=180/9

x=20

hence,

first angle =2x°=2×20 =40°

second angle =3x°=3×20=60°

third angle =4x°=4×20=80°

therefore,measure of smallest angle of the triangle is 40°

Answer 2

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

We know, sum of angles is 180

So,

→ 2x + 3x + 4x = 180

→ 9x = 180

→ x = 180/9

→ x = 20

Angles :-

2x = 2 × 20 = 40°

3x = 3 × 20 = 60°

4x = 4 × 20 = 80°

____________________________

Smallest → 40°