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

In the following figure,ray $YW$ stands on a line $XYZ$. $\angle WYZ : \angle WYX = 1 : 2$. Ray $YQ$ and ray $YP$ are angle bisectors of $\angle WYZ$ and $\angle WYX$ respectively. Find $\angle PYQ$. (in $^{\circ}$)

In the following figure,lines $AB$ and $CD$ intersect each other at point $P$. If $\angle APC : \angle BPC = 7 : 8$,find all the angles.

In the following figure,ray $BA$ is perpendicular to line $CD$. If $x: y: z = 4: 5: 6$,then find the values of $x, y,$ and $z$.

In the following figure,lines $AB$ and $CD$ intersect at $O.$ If $\angle AOC + \angle BOE = 100^{\circ}$ and $\angle BOD = 40^{\circ},$ find $\angle BOE$ and reflex $\angle COE.$

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