The measures of two adjacent angles of a quadrilateral are $52°$ and $110°.$ The remaining two adjacent angles are equal. Find the measure of each of these equal angles.

A quadrilateral has three acute angles each measuring $85°.$ Find the measure of the fourth angle. (Without the degree symbol)

The bisectors of $\angle \mathrm{A}$ and $\angle \mathrm{B}$ meet at point $\mathrm{P}.$ If $\angle C=50°$ and $\angle \mathrm{D}=100°,$ find the measure of $\angle \mathrm{APB}$.

In a quadrilateral, $\mathrm{CO}$ and $\mathrm{DO}$ are the bisectors of $\angle \mathrm{C}$ and $\angle \mathrm{D}$ respectively.

Prove that $\angle \mathrm{A}+\angle \mathrm{B}=2\angle \mathrm{COD}$.