Răspuns :
[tex]Trebuie\ sa\ aflam\ toate\ unghiurile\ in\ functie\ de\ C:\\
\{A,B,C\} d.p.\{4,5,6\} \Rightarrow\frac{A}{4}=\frac{B}{5}=\frac{C}{6}\Rightarrow A=\frac{4C}{6}, B=\frac{5C}{6}\\
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\{C,D\} d.p. \{14,5\}\Rightarrow\frac{C}{14}=\frac{D}{5}\Rightarrow D=\frac{5C}{14}\\
A+B+C+D=360\\
\\
\frac{4C}{6}+\frac{5C}{6}+C+\frac{5C}{14}=360 |\cdot 42\\
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28C+35C+42C+15C=15120\\
120C=15120\Rightarrow \boxed{C=126}\\
A=\frac{4\cdot126}{6}=\boxed{84}\\
\\
B=\frac{5\cdot 126}{6}=\boxed{105}\\
\\
[/tex]
[tex]D=\frac{5\cdot 126}{14}=\boxed{45}[/tex]
[tex]D=\frac{5\cdot 126}{14}=\boxed{45}[/tex]
Notez cu A masura unghiului A ,respectiv cu B,C, si D ale unghiurilor B,C,D . A=B=C 4 5 6 C=D 14 5 Mai stiu ca suma unghiruilor intr-un patrulater este de 360 de grade. A+B+C+D=360 Scot pe A,B si D in functie de C A=4C 6 B=5C 6 C=5C 14 Înlocuiesc in suma si am: 4C +5C+5C+C=360 6 6 14 Aduc la accelasi numitor:84 14*4C+14*5C+6*5C+84C =360 84 56C+7-C+30C+84C=360*84 240C=360*84 C=360*84:240 C=126 A=4*126:6=84 B=5*126:6=105 D=5*126:14=25
