## PROBLEM 4

Lines $AB$ and $CD$ intersect at $O$. Knowing that rays $[OM$, $[OT$, $[OR$ are the bisectors of angles $\angle BOD$, $\angle DOM$, and respectively $\angle COB$, and $m(\angle AOM)=130^{\circ}$, calculate:
a) $m(\angle ROM)$ and $m(\angle AOD)$;

b) the measure of the angle between the bisectors of angles $\angle AOC$ and $\angle BOR$.
## Solution:

a)
Diagram. point
$m(\angle R O M)=90^{\circ}$ ..... point
$m(\angle A O D)=30^{\circ}$ ..... point
b) Notation of the angle bisectors and explanation ..... 2 points
$\angle A O C \equiv \angle D O B$ (vertical angles). ..... point
Completion point