In $\Delta XYZ$,$\angle X : \angle Y : \angle Z = 1 : 4 : 4$,then $\angle Z = \ldots$ (in $^{\circ}$)

$ABC$ and $DBC$ are two isosceles triangles on the same base $BC$ (see figure). Show that $\angle ABD = \angle ACD$.

Can a triangle have two obtuse angles? Give reason for your answer.

Side $QR$ of $\Delta PQR$ is extended on both the sides so that exterior angles $\angle PQS$ and $\angle PRT$ are formed. If $\angle PQS = 100^{\circ}$ and $\angle PRT = 130^{\circ}$,find the measure of each angle of $\Delta PQR$.

In $\Delta PQR$,$PQ = PR$. If $\angle Q = 48^{\circ}$,then find $\angle P$ and $\angle R$.

An exterior angle of a triangle is $105^{\circ}$ and its two interior opposite angles are equal. Each of these equal angles is