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

If in $\Delta XYZ$,$\angle Y > \angle X > \angle Z$,then find the smallest side of the triangle.

Bisectors of the angles $B$ and $C$ of an isosceles triangle $ABC$ with $AB = AC$ intersect each other at $O$. Show that the external angle adjacent to $\angle ABC$ is equal to $\angle BOC$.

In $\Delta ABC$,the bisectors of $\angle B$ and $\angle C$ intersect at $P$. $A$ line drawn through $P$ and parallel to $BC$ intersects $AB$ at $X$ and $AC$ at $Y$. Prove that $XY = XB + YC$.

In the given figure,$AB \perp BQ$,$PQ \perp QB$,$AC = PR$ and $BR = QC$. Prove that $\angle BAC = \angle QPR$.

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