Prove that the interior angle of a regular pentagon is three times the exterior angle of a regular decagon.

Two regular polygons are such that the ratio between their number of sides is $1:3$ and the ratio of measure of their interior angles is $3:5$. Find the number of sides of each polygon.

In the figure of kite, find the values of $x$ and $y$.

In the following parallelogram, find the values of $x$ and $y$.

If four angles of a quadrilateral are $2:5:6:7$ then find the angles of the quadrilateral.