The angles of a triangle have the ratio 3:2:1. What is the measure of the smallest angle?

2 Answers
Jun 9, 2018

30^@

Explanation:

"the sum of the angles in a triangle "=180^@

"sum the parts of the ratio "3+2+1=6" parts"

180^@/6=30^@larrcolor(blue)"1 part"

3" parts "=3xx30^@=90^@

2" parts "=2xx30^@=60^@

"the smallest angle "=30^@

Jun 9, 2018

The smallest angle is /_C=30°

Explanation:

Let the triangle be DeltaABC 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 = 180/6

:. 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°.