Prove that the interior angle of a regular five-sided polygon (pentagon) is three times the exterior angle of a regular decagon.
 

Determine the number of sides of a polygon whose exterior and interior angles are in the ratio $1:5$.

In the given quadrilateral $ABCD, AO$ and $BO$ are the bisectors of $\angle A$ and $\angle B$ respectively. Prove that $\angle AOB=\frac{1}{2}(\angle C+\angle D)$.

In the given figure, $QSTW$ and $STRW$ are parallelograms. If  $\mathrm{ST}=8 \mathrm{cm}$ , find the lengths of $QW$ and $WR$. 

Find the values of  $\mathrm{x}, \mathrm{y}$ and $\mathrm{z}$ in the given parallelogram.