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

In $\Delta ABC$ and $\Delta PQR$,if $\angle B = \angle P = 90^{\circ}$,$AC = RQ$,and $AB = RP$,then $\Delta ABC \cong \Delta \ldots \ldots \ldots$

Show that in a quadrilateral $ABCD$,$AB + BC + CD + DA < 2(BD + AC)$.

In $\Delta ABC$ and $\Delta PQR$,$AB = PR$,$BC = RQ$ and $\angle B = \angle R$,then $\Delta ABC \cong \Delta \ldots$

In $\Delta PQR$,$PQ = 7.5 \, cm$,$QR = 6.2 \, cm$ and $a < PR < b$,then find the values of $a$ and $b$ in $cm$.

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 $\triangle PNX \cong \triangle QMX$.