Question

The angles of a triangle are in the ratio 3:2:1 . Find the angles.​

Answer 1

The smallest angle is ∠C=30°

Let the triangle be ΔABC and angles be ∠A,∠B,∠C

Now, we know that all the 3 angles of a triangle sum up to be 180° from the Triangle Sum Property.

∴∠A+∠B+∠C=180

∴3x+2x+x=180 ... [Given that the ratio of angles is 3:2:1]

∴6x=180

∴x=1806

∴x=30°

Now assigning the angles their values,

∠A=3x=3(30)=90°

∠B=2x=2(30)=60°

∠C=x=(30)=30°

Now, as we can clearly observe, the smallest angle is ∠C

which is =30°

Hence, the smallest angle is of 30

Answer 2

Answer:

let the angles= 3x, 2x, 1x

we know that sum of triangle = 180

3x+2x+1x=180

6x= 180

x= 30

3x=90

2x=60

1x= 30