Two adjactent angles of parallelogram $\mathrm{PQRS}$ are in the ratio $2:7$. Find all the angles of the parallelogram.

$\mathrm{TALK}$ is a parallelogram. Diagonals $\mathrm{AK}$ and $\mathrm{TL}$ meet at $\mathrm{O}$. $\mathrm{BX}$ is a line segement through $\mathrm{O}$. Give reasons for the following:

$\mathrm{OA}=\mathrm{OK}$

$\mathrm{TALK}$ is a parallelogram. Diagonals $\mathrm{AK}$ and $\mathrm{TL}$ meet at $\mathrm{O}$. $\mathrm{BX}$ is a line segement through $\mathrm{O}$. Give reasons for the following:

$\angle \mathrm{OAX}=\angle \mathrm{OKB}$

$\mathrm{TALK}$ is a parallelogram. Diagonals $\mathrm{AK}$ and $\mathrm{TL}$ meet at $\mathrm{O}$. $\mathrm{BX}$ is a line segement through $\mathrm{O}$. Give reasons for the following:

$\angle \mathrm{AOX}=\angle \mathrm{KOB}$