The exterior angle of a regular polygon is one-fifth of its interior angle. How many sides the polygon has?

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.

In the adjacent figure, bisectors of $\angle P$ and $\angle Q$ meet at a point $M$. If $\angle R=110°$ and $\angle S=60°$, then find the measure of $\angle PMQ$.

In a quadrilateral $ABCD$, $CO$ and $DO$ are the bisector of $\angle C$ and $\angle D$ respectively. Prove that $\angle COD=\frac{1}{2}\left(\angle A+\angle B\right)$.