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

2 Answers
Jun 9, 2018

Answer:

#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

Answer:

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°#.