The angles of a triangle are in the ratio $2: 3: 4$. Find the angles of the triangle.

Given: Ratio of angles is $2: 3: 4$.
To find: Angles of the triangle.
Let the angles of the triangle be $\angle A, \angle B,$ and $\angle C$.
Therefore,$\angle A = 2x$,$\angle B = 3x$,and $\angle C = 4x$.
In $\triangle ABC$,the sum of angles is $\angle A + \angle B + \angle C = 180^{\circ}$ (Angle Sum Property of a triangle).
Substituting the values: $2x + 3x + 4x = 180^{\circ}$.
$9x = 180^{\circ} \Rightarrow x = 180^{\circ} / 9 = 20^{\circ}$.
Therefore,$\angle A = 2 \times 20^{\circ} = 40^{\circ}$,$\angle B = 3 \times 20^{\circ} = 60^{\circ}$,and $\angle C = 4 \times 20^{\circ} = 80^{\circ}$.
Hence,the angles of the triangle are $40^{\circ}, 60^{\circ},$ and $80^{\circ}$.