Question

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

Answer 1

Let the smallest angle of the triangle be $\angle C$ and let $\angle A=2\angle C\text{and}\angle B=3\angle C$.
Then,
$$\begin{gathered} \angle A+\angle B+\angle C=180°\left[\text{Sum of the angles of a triangle}\right] \\ \Rightarrow 2\angle C+3\angle C+\angle C=180° \\ \Rightarrow 6\angle =180° \\ \Rightarrow \angle C=30° \end{gathered}$$

$\therefore \angle A=2\angle C$
$$\begin{gathered} =2\left(30\right)° \\ =60° \end{gathered}$$
Also,
$$\begin{gathered} \angle B=3\angle C \\ =3\left(30\right)° \\ =90° \end{gathered}$$