[tex]\bold{a)} \ \alpha+\beta=180^o \\ \alpha=\frac{1}{3} \ din \ \beta=\frac{\beta}{3} \\ \Rightarrow \beta=3\alpha \\ \alpha+3\alpha=4\alpha=180^o \\ \Rightarrow \alpha=\frac{180^o}{4} =\boxed{45^o}; \\ \Rightarrow \boxed{\beta=135^o};[/tex]
[tex]\bold{b)} \ \alpha+\beta=90^o \\ \alpha=\frac{2}{7} \ din \ \beta=\frac{2\beta}{7} \\ \Rightarrow \frac{2\beta}{7}+\frac{7\beta}{7}=90^o \\ \Rightarrow 9\beta=7\cdot 90^o=630^o \\ \Rightarrow \beta=\frac{630^o}{9}=\boxed{70^o} \\ \Rightarrow \boxed{\alpha=20^o}[/tex]
