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

Jun 9, 2018

${30}^{\circ}$

Explanation:

$\text{the sum of the angles in a triangle } = {180}^{\circ}$

$\text{sum the parts of the ratio "3+2+1=6" parts}$

${180}^{\circ} / 6 = {30}^{\circ} \leftarrow \textcolor{b l u e}{\text{1 part}}$

$3 \text{ parts } = 3 \times {30}^{\circ} = {90}^{\circ}$

$2 \text{ parts } = 2 \times {30}^{\circ} = {60}^{\circ}$

$\text{the smallest angle } = {30}^{\circ}$

Jun 9, 2018

The smallest angle is /_C=30°

Explanation:

Let the triangle be $\Delta A B C$ and angles be $\angle A , \angle B , \angle C$

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

$\therefore \angle A + \angle B + \angle C = 180$

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

$\therefore 6 x = 180$

$\therefore x = \frac{180}{6}$

:. 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 $\angle C$

which is =30°

Hence, the smallest angle is of 30°.