[tex]\text{Suma unghiurilor unui patrulater convex ABCD este: } \\ .\;\;\;\;\;\;\;\;\;\; A+B+C+D=360^o \\ a) \\ \frac{A}{3}= \frac{B}{4}=\frac{C}{8}=\frac{D}{9}=k \;\;=\ \textgreater \ \;\; A=3k;\;\;\;B=4k;\;\;\;C=8k;\;\;\; D=9k \\ A+B+C+D=360 \;\;=\ \textgreater \ \;\;3k+4k+8k+9k=360 \\ 24k=360\;\;\;=\ \textgreater \ \;\;\;k= \frac{360}{24} =15 \\ A=3k=3*15=\boxed{45^o} \\ B=4k=4*15=\boxed{60^o} \\ C=8k=8*15=\boxed{120^o} \\ D=9k=9*15=\boxed{135^o}[/tex]
[tex]b) \\ A \cdot 1=B \cdot 0,5=C \cdot 0,(3)=D \cdot 0,25 \\ A= \frac{B}{2}= \frac{C}{3}=\frac{D}{4}=k \\ A=k;\;\;\;B=2k;\;\;\;C=3k;\;\;\;D=4k \\ A+B+C+D=360\;\;\;=\ \textgreater \ \;\;\; k+2k+3k+4k=360 \\ 10k=360 \;\;\;=\ \textgreater \ \;\;\;k= \frac{360}{10} =36 \\ A=k=\boxed{36^o} \\ B=2k=2 \cdot 36=\boxed{72^o} \\ C=3k=3 \cdot 36=\boxed{108^o} \\ D=4k=4 \cdot 36=\boxed{144^o}[/tex]
