4. Let $\Varangle A O D$ with $m(\Varangle A O D)=98^{\circ}$ and $(O B,(O C$ half-lines included in the interior of $\Varangle A O D$, (OC half-line included in the interior of $\Varangle B O D$ such that

$$
a \cdot m(\Varangle A O B)=c \cdot m(\Varangle B O C) \text { and } b \cdot m(\Varangle B O C)=c \cdot m(\Varangle C O D) \text {, }
$$

where $a, b, c$ are prime numbers that satisfy the relation $3 a+5(3 b+7 c)=195$.

Find $m(\Varangle A O B), m(\Varangle B O C)$, and $m(\Varangle C O D)$.

Carmen Botea and Viorel Botea, Brăila
Solution. $3 a+5(3 b+7 c)=195 \Rightarrow a=5 \Rightarrow 5(3 b+7 c)=180 \Rightarrow c=3 \Rightarrow b=5$

$$
\begin{aligned}
& \text { It follows that }\left\{\begin{array}{l}
m(\angle A O B)+m(\angle B O C)+m(\angle C O D)=98^{\circ} \\
5 \cdot m(\angle A O B)=3 \cdot m(B O C) \\
5 \cdot m(\angle B O C)=3 \cdot m(C O D)
\end{array}\right. \\
& \Rightarrow m(\angle A O B)=18^{\circ} \Rightarrow m(\angle B O C)=30^{\circ} \Rightarrow m(\angle C O D)=50^{\circ} .
\end{aligned}
$$