In the figure,$DE \parallel QR$ and $AP$ and $BP$ are bisectors of $\angle EAB$ and $\angle RBA$ respectively. Find $\angle APB.$ (in $^{\circ}$)

Let $OA, OB, OC$ and $OD$ be rays in the anticlockwise direction such that $\angle AOB = 100^{\circ}, \angle COD = 100^{\circ}, \angle BOC = 82^{\circ}$ and $\angle AOD = 78^{\circ}$. Is it true to say that $AOC$ and $BOD$ are lines?

Lines $AB$ and $CD$ intersect at $P$. If $\angle APC = 2x + 30^{\circ}$ and $\angle BPD = 4x - 20^{\circ}$,then find $x$,$\angle APC$,and $\angle BPD$.

$\angle ABC$ and $\angle ABD$ are a linear pair of angles. If $\angle ABC : \angle ABD = 17 : 13$,then find $\angle ABC$ and $\angle ABD$.

In the figure,$AB$,$CD$,and $EF$ are three lines concurrent at $O$. Find the value of $y$. (in $^{\circ}$)

$\angle PRT$ is an exterior angle of $\Delta PQR$. If $\angle P = 70^{\circ}$ and $\angle Q = 50^{\circ}$,then $\angle PRT = \ldots$ (in $^{\circ}$)