Of the three angles of a triangle, one is twice the smallest and another one is thrice the smallest.

Question:

Of the three angles of a triangle, one is twice the smallest and another one is thrice the smallest. Find the angles.

Solution:

Let the smallest angle of the triangle be $\angle C$ and let $\angle A=2 \angle C$ and $\angle B=3 \angle C$.

Then,

$\angle A+\angle B+\angle C=180^{\circ} \quad$ [Sum of the angles of a triangle]

$\Rightarrow 2 \angle C+3 \angle C+\angle C=180^{\circ}$

$\Rightarrow 6 \angle=180^{\circ}$

$\Rightarrow \angle C=30^{\circ}$

$\therefore \angle A=2 \angle C$

$=2(30)^{\circ}$

$=60^{\circ}$

Also,

$\angle B=3 \angle C$

$=3(30)^{\circ}$

$=90^{\circ}$

 

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