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

Given:

An angle of a parallelogram is two-third of its adjacent angle.

To do:

We have to find the measure of each of the angles of the parallelogram. 

Solution: 

 Let the measure of the adjacent angle be $3x$.

This implies,

The measure of the angle $=\frac{2}{3}\times3x=2x$. 

We know that,

Sum of the angles in a parallelogram is $360^o$ and opposite angles of a parallelogram are equal.

Therefore,

The four angles of the parallelogram are $2x, 3x, 2x$ and $3x$.

$2x+3x+2x+3x=360^o$

$10x=360^o$

$x=\frac{360^o}{10}$

$x=36^o$

$\Rightarrow 2x=2(36^o)=72^o$

$\Rightarrow 3x=3(36^o)=108^o$

The measure of all the angles of the parallelogram is $72^o, 108^o, 72^o$ and $108^o$.