Can a triangle have three angles less than $60°$ $?$

In $△ABC$, if $2\angle A=3\angle B=6\angle C,$ calculate the measure of $\angle A, \angle B$ and $\angle C$.

$($ Hint: Let $2\angle A=3\angle B=6\angle C=x\Rightarrow \angle A=\frac{x}{2}, \angle B=\frac{x}{3},\angle C=\frac{x}{6}$$)$

In the following figure, the sides $AB$ and $AC$ of $△ABC$ are produced to $P$ and $Q$, respectively. The bisectors of $\angle PBC$ and $\angle QCB$ intersect at $O$. Prove that $\angle BOC=90°-\frac{1}{2}\angle BAC$.

In the following figure, $\angle BAC=90°, \angle ADC=90°$. Find the length of $AB$.

There is a slide in a park. One of its side walls has been painted in green colour with message 'KEEP THE PARK GREEN AND CLEAN'. If the sides of the walls are $15 \mathrm{m}, 11 \mathrm{m},$ and $6 \mathrm{m}$, find the perimeter of the shaded portion. Do you keep your surroundings green and clean $?$