Problem 1. The angles $\Varangle A O B$ and $\Varangle B O C$ are supplementary, and the measure of the first is five times greater than the measure of the second. Determine the measure of the angle formed by the bisectors of the angles $\Varangle A O B$ and $\Varangle B O C$.
## Solution and Grading

If the angles $\Varangle A O B$ and $\Varangle B O C$ are adjacent, the measure of the angle formed by their bisectors is

90 $2 \mathrm{p}$

$m(\Varangle A O B)=150^{\circ}$ and $m(\Varangle B O C)=30$ $2 \mathrm{p}$

If the angles $\Varangle A O B$ and $\Varangle B O C$ are non-adjacent, the measure of the angle formed by their bisectors is 60 $3 \mathrm{p}$