## Subject IV. (30 points)

Inside the angle $\Varangle A O B$, points $A_{1}, A_{2}, A_{3}, \ldots, A_{101}$ are taken such that: $m\left(\Varangle A O A_{1}\right)=m\left(\Varangle A_{1} O A_{2}\right)=m\left(\Varangle A_{2} O A_{3}\right)=\ldots=m\left(\Varangle A_{101} O B\right)=1^{\circ} 20^{\prime}$.

a) Find the measure of the angle $\Varangle A O B$.

b) If $M$ is a point inside the angle $\Varangle A O B$ such that $O M \perp O B$, find $m\left(\varangle A_{12} O M\right)$.

Prof. Teodor Poenaru, Nicolae Bălcescu Theoretical High School, Cluj-Napoca

All questions are mandatory. 10 points are awarded by default.

SUCCESS!

Effective working time - 2 hours.

## Grading Scale for 6th Grade (OLM 2014 - Local Stage)

## Of. $10 \mathrm{p}$
## Subject IV.

a) $m(\Varangle A O B)=102 \cdot 1^{\circ} 20^{\prime}=102^{\circ} 2040^{\prime}=136^{\circ}$

(20p)
b) $m(\Varangle A O M)=136^{\circ}-90^{\circ}=46^{\circ}$

$m\left(\Varangle A O A_{12}\right)=12 \cdot 1^{\circ} 20^{\prime}=16^{\circ}$

$m\left(\Varangle A_{12} O M\right)=46^{\circ}-14^{\circ}=30^{\circ}$