Apply $45-45-90$ degree triangle sides formula to find the other sides of a triangle whose one side is $8\sqrt{2} \mathrm{cm}$

Circles $C_1$ and $C_2,$ of radii $r$ and $R$ respectively, touch each other as shown in the figure. The line $l$ which is parallel to the line joining the centres of $C_1$ and $C_2,$ is tangent to $C_1$ at $P$ and intersects $C_2$ at $A,B$. If $R^2=2r^2,$ then $\angle AOB$ equals-

The vertical angle of an isosceles triangle is $90°$. If each of its base angles is $k°$ then find the value of $k$.

If the value of angle $x$ is $k°$ in the following figure then find the value of $k$.

In the figure, $LM=LN, \angle FNL=110°$. If the value of  $\angle LMN$ is $k°$ then find the value of $k$.

In $△ABC , AB=AC$ and $\angle B=50°$ . Then $\angle C=$

In the figure, $LM=LN, \angle FNL=110°$. If the value of $\angle MLN$ is $k°$ then find the value of $k$.