2. Given the obtuse angle $\Varangle A O B$ and points $C$ and $D$ located in opposite half-planes relative to the line $A B$ such that $m(\Varangle C O D)=80^{\circ}$. If $[O N$ is the bisector of angle $\Varangle A O C$, $[O M$ is the bisector of angle $\Varangle B O D$, and $m(\Varangle B O C)=150^{\circ}$, then calculate the measure of angle $\Varangle M O N$.

Supliment, G.M. , November 2013
## Solution:

$$
\begin{array}{ll}
m(\angle NOA)=(180^{\circ}-150^{\circ}): 2=15^{\circ} \\
m(\angle AOD)=80^{\circ}-30^{\circ}=50^{\circ} & 2p \\
m(\angle BOD)=(180^{\circ}-50^{\circ}): 2=65^{\circ} & 2p
\end{array}
$$

Completion $m(\angle MON)=130^{\circ}$