In $\Delta ABC$,if $\angle A = \angle B = \angle C$,then $\angle B = \dots$ (in $^{\circ}$)

In the figure,$OD$ is the bisector of $\angle AOC$,$OE$ is the bisector of $\angle BOC$,and $OD \perp OE$. Show that the points $A, O$,and $B$ are collinear.

$\angle ABD$ and $\angle ACE$ are exterior angles of $\Delta ABC$. If $\angle ABD = 140^{\circ}$ and $\angle ACE = 80^{\circ}$,then find $\angle A$. (in $^{\circ}$)

In $\Delta ABC$,the bisectors of $\angle B$ and $\angle C$ intersect each other at $I$. Prove that $\angle BIC = 90^{\circ} + \frac{1}{2} \angle A$.

In the figure,if $AB \parallel CD$,$\angle BMX = 125^{\circ}$ and $\angle CNX = 55^{\circ}$,find $\angle MXN$. (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 $^{\circ}$)