If an angle of a parallelogram is two-third of its adjacent angle, find the angles of the parallelogram.

Let the measure of the adjacent angle be x. Then, the other angle will be $\dfrac{2x}{3}$.

We know that,

Sum of its adjacent angles of a //gm = 180°.

$\Rightarrow x + \dfrac{2x}{3} = 180^{\circ} \\[1em] \Rightarrow \dfrac{3x + 2x}{3} = 180^{\circ} \\[1em] \Rightarrow \dfrac{5x}{3} = 180^{\circ} \\[1em] \Rightarrow 5x = 540^{\circ} \\[1em] \Rightarrow x = \dfrac{540^{\circ}}{5} \\[1em] \Rightarrow x = 108^{\circ}$

∴ x = 108°.

⇒ $\dfrac{2x}{3} = \dfrac{2}{3} \times 108°$ = 72°

Since opposite angles in a parallelogram are equal, the four angles are : 72°, 108°, 72°, and 108°.

Hence, angles of the parallelogram are 72°, 108°, 72°, and 108°.