Prove that sum of all the angles around a point is $360°$.

In the figure, $\mathrm{A}\mathrm{O}\mathrm{B}$ is a line. Ray $\mathrm{O}\mathrm{C}$ stands on $\mathrm{A}\mathrm{B}$. $\mathrm{O}\mathrm{D}$ and $\mathrm{O}\mathrm{E}$ are bisectors of $\angle \mathrm{A}\mathrm{O}\mathrm{C}$ and $\angle \mathrm{B}\mathrm{O}\mathrm{C}$ respectively. Prove that $\angle \mathrm{D}\mathrm{O}\mathrm{E}\mathrm{}=\mathrm{}90°$.

In the figure, $x:y:z=1:3:4$. If $\mathrm{A}\mathrm{O}\mathrm{B}$ is a straight line, find the value of $x,y$ and $z$.

Find $\angle AOC$, $\mathrm{\angle }\mathrm{B}\mathrm{O}\mathrm{D}$ and $\mathrm{\angle }\mathrm{A}\mathrm{O}\mathrm{E}$ in the figure, it is being given that $\mathrm{\angle }\mathrm{C}\mathrm{O}\mathrm{D}=90°, \mathrm{\angle }\mathrm{B}\mathrm{O}\mathrm{E}=72°$ and $\mathrm{A}\mathrm{O}\mathrm{B}$ is a straight line.