G3.1 In figure $1, M N$ is a straight line, $\angle Q O N=a^{\circ}, \angle P O Q=b^{\circ}$ and $\angle P O M=c^{\circ}$. If $b: a=2: 1$ and $c: b=3: 1$, find the value of $b$.
$\begin{array}{l}b=2 a, c=3 b=6 a \\ a+b+c=180(\mathrm{adj} . \angle \mathrm{s} \text { on st. line }) \\ a+2 a+6 a=180 \Rightarrow a=20 \\ b=2 a=40\end{array}$