Each of the two equal angles of an isosceles triangle are twice the third angle. Find the measure of all the angles of the triangle.

One of the acute angles of a right-angled triangle is $47°$. Find the measure of the other acute angle.

Is it possible to have $64°,36° \text{and} 80°$ as angles of a triangle? Give reasons.

Is it possible to have a triangle with sides $5 \mathrm{cm},6 \mathrm{cm} \text{and} 11 \mathrm{cm}$? Give reasons.

In the given figure, if $\angle R=43°,\angle RST=94° \text{and} \angle T=32°$, find $\angle P$.

$P$ is a point in the exterior of $∆XYZ$ as shown in the figure. $PX,PY$ and $PZ$ are joined.

Is $XY+YZ>ZX$? Why?

$P$ is a point in the exterior of $∆XYZ$ as shown in the figure. $PX,PY$ and $PZ$ are joined.

Is $PX+PY>XY$? Why? 

$P$ is a point in the exterior of $∆XYZ$ as shown in the figure. $PX,PY$ and $PZ$ are joined.

Is $PX+PZ>XZ$? Why?

$P$ is a point in the exterior of $∆XYZ$ as shown in the figure. $PX,PY$ and $PZ$ are joined.

Is $PY+PZ>YZ$? Why?