$\angle PRT$ is an exterior angle of $\Delta PQR$. If $\angle P = 70^{\circ}$ and $\angle Q = 50^{\circ}$,then $\angle PRT = \ldots$ (in $^{\circ}$)

Measure of each exterior angle of an equilateral triangle is $\ldots \ldots \ldots$ (in $^{\circ}$)

In a huge park,people are concentrated at three points (see Fig) :
$A$ : where there are different slides and swings for children,
$B$ : near which a man-made lake is situated,
$C$ : which is near to a large parking and exit. Where should an ice cream parlour be set up so that the maximum number of persons can approach it?
(Hint: The parlour should be equidistant from $A$,$B$,and $C$.)

In $\Delta ABC$,$AB = AC$,$\angle A = 2x^{\circ}$ and $\angle B = x + 10^{\circ}$. Find each of the angles of $\Delta ABC$.

In a triangle $ABC$,$D$ is the mid-point of side $AC$ such that $BD = \frac{1}{2} AC$. Show that $\angle ABC$ is a right angle.

Prove that in a triangle,other than an equilateral triangle,the angle opposite to the longest side is greater than $\frac{2}{3}$ of a right angle.