Angle Sum Property of a Quadrilateral

If the bisectors of two adjacent angles $A$ and $B$ of a quadrilateral $ABCD$ intersect at a point $O$ such that $\angle C+\angle D=k\angle AOB$, then find the value of $k$.

In a quadrilateral $ABCD,$ bisectors of angles $A$ and $B$ intersect at $O$ such that $\angle AOB=75°$. If the value of $\angle C+\angle D$ is $k°$, then find the value of $k$.

If the angles of a quadrilateral are in the ratio $3: 5: 9: 13$, then find the measure of the smallest angle. (Write the answer without degree symbol)

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

The angles of a quadrilateral are in the ratio $3:5:9:13$. Find all the angles of the quadrilateral.

In a quadrilateral $ABCD$, the angles $A\mathit{,}B\mathit{,}C$ and $D$ are in the ratio $1:2:4:5$. Find the measure of each angle of the quadrilateral.

Three angles of a quadrilateral are respectively equal to $110°, 50°$ and $40°$. Let its fourth angle is $k°$, find the value of $k$.

In a quadrilateral $ABCD, \angle A+\angle C$ is $2$ times $\angle B+\angle D$. If $\angle A=140°$ and $\angle D=60°$, then $\angle B=$?

If the degree measures of the angles of quadrilateral are $4x, 7x, 9x$ and $10x$, what is the sum of the measures of the smallest angle and largest angle?