In $\Delta ABC$,$AB = AC$ and $\angle C = 75^{\circ}$,then find $\angle B$. (in $^{\circ}$)

In $\triangle ABC$,$AB = AC$ and $\angle B = 50^{\circ}$. Then $\angle C$ is equal to (in $^{\circ}$)

In the given figure,$PS = QR$ and $PR = QS$. Prove that $(1) \angle PSQ = \angle QRP$ and $(2) \angle SPQ = \angle RQP$.

In the given figure,$PN$ and $QM$ are both perpendicular to line segment $PQ$. Also,$X$ is the midpoint of $PQ$ as well as $MN$. Prove that $\triangle PNX \cong \triangle QMX$.

In the given figure,$PQ = PR$ and $\angle Q = \angle R$. Prove that $\triangle PQS \cong \triangle PRT$.

$\angle ABD$ and $\angle ACE$ are exterior angles of $\Delta ABC$. If $\angle ABD = 110^{\circ}$ and $\angle ACE = 150^{\circ}$,then $\angle A$ is: (in $^{\circ}$)