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

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

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Answer 1 · 2018-06-09T12:52:10

$30^{\circ}$ $30^@$

Explanation:

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

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

$\frac{180^{\circ}}{6} = 30^{\circ} \leftarrow 1 part$ $180^@/6=30^@larrcolor(blue)"1 part"$

$3 parts = 3 \times 30^{\circ} = 90^{\circ}$ $3" parts "=3xx30^@=90^@$

$2 parts = 2 \times 30^{\circ} = 60^{\circ}$ $2" parts "=2xx30^@=60^@$

$the smallest angle = 30^{\circ}$ $"the smallest angle "=30^@$

Answer 2 · 2018-06-09T12:55:10

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 $30°$ .

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

2 Answers

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