## SUBJECT 3

Around point $O$, angles AOB, BOC, COD, DOA are formed. It is known that $\varangle A O B$ and $\varangle B O C$ are complementary, and $\varangle A O B$ and $\varangle C O D$ are supplementary. If [OM is the bisector of $\varangle B O C$, [ON is the bisector of $\varangle C O D$, and [OP is the bisector of $\varangle A O D$, find:
a) $m(\varangle N O P)$.
b) $m(\varangle A O B)$, given that $m(\varangle P O M)=132^{\circ}$.
c) $m(\varangle A O B)$, given that $m(\varangle C O D)$ is 4 times larger than $m(\varangle B O C)$.

S.G.M. 2014
## SUBJECT 3

Around point $O$, angles AOB, BOC, COD, DOA are formed. It is known that $\varangle A O B$ and $\varangle B O C$ are complementary, and $\varangle A O B$ and $\varangle C O D$ are supplementary. If [OM is the bisector of $\varangle B O C$, [ON is the bisector of $\varangle C O D$, and [OP is the bisector of $\varangle A O D$, find:
a) $\mathrm{m}(\varangle \mathrm{NOP})$.
b) $\mathrm{m}(\varangle \mathrm{AOB})$, knowing that $\mathrm{m}(\varangle \mathrm{POM})=132^{\circ}$.
c) $m(\varangle A O B)$, knowing that $m(\varangle C O D)$ is 4 times larger than $m(\varangle B O C)$.

| A | a) $m(\varangle N O P)=\left(360^{\circ}-90^{\circ}\right): 2=135^{\circ}$. |
| :--- | :--- | :--- |