If an angle of a parallelogram is two-third of its adjacent angle,

Two adjacent angles of a parallelogram add up to $180^{\circ}$.

Let $x$ be the angle.

$\therefore x+\frac{2 x}{3}=180^{\circ}$

$\frac{5 x}{3}==180^{\circ}$

$x=72^{\circ}$

$\frac{2 x}{3}=\frac{2 \times 72^{\circ}}{3}=108^{\circ}$

Thus, two of the angles in the parallelogram are $108^{\circ}$ and the other two are $72^{\circ}$.