Notez cu A masura unghiului A , respectiv cu B, C , si D ale unghiurilor B , C , D.
[tex]\frac{a}{4} = \frac{b}{5} = \frac{c}{6}[/tex]
[tex]6\cdot c=4\cdot d[/tex]
suma unghiurilor intr-un patrulater este de 360°
a + b + c + d = 360
Scot pe a , b si d in functie de c
[tex]a = \frac{4c}{6}[/tex]
[tex]b = \frac{5c}{6}[/tex]
[tex]d =\frac{6c}{4}[/tex]
Inlocuiesc in suma si am:
[tex]\frac{4c}{6}+\frac{5c}{6}+c+ \frac{6c}{4}=360[/tex]
[tex]9c\cdot 4+24\cdot c+36c=360\cdot6\cdot4\\ \\36c+24c+36c=360\cdot24\\ \\96c=8640\\ \\c = 8640:96\\ \\c=90[/tex]
[tex]a = \frac{4c}{6}=(4\cdot90):6=60\\ \\ b = \frac{5c}{6}=(5\cdot90):6=75\\ \\d =\frac{6c}{4}=(6\cdot90):4=135[/tex]
verificare
a + b + c + d = 360
60 + 75 + 90 + 135 = 360
360 = 360
