Question

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

Answer 1

`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^@`

Answer 2

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°`.