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

Write the measures of the sides of $\Delta PQR$ in ascending order,given that $\angle P = 40^{\circ}$ and $\angle R = 80^{\circ}$.

In the given figure,$l \parallel m$ and $M$ is the mid-point of a line segment $AB$. Show that $M$ is also the mid-point of any line segment $CD,$ having its end points on $l$ and $m,$ respectively.

In $\Delta ABC$, $\angle B = \angle C$, $AB = 5 \text{ cm}$, and $BC = 8 \text{ cm}$. Then, the perimeter of $\Delta ABC$ is: (in $\text{ cm}$)

In $\Delta ABC$,$AB = AC$. If $\angle A = 50^{\circ}$,then find $\angle B$ and $\angle C$.

The image of an object placed at a point $A$ before a plane mirror $LM$ is seen at the point $B$ by an observer at $D$ as shown in the figure. Prove that the image is as far behind the mirror as the object is in front of the mirror.