Răspuns:
[tex]\alpha = 70^o, \beta = 80^o, \gamma = 90^o, \theta = 120^o[/tex]
Explicație pas cu pas:
Fie [tex]\alpha, \beta, \gamma, \theta[/tex] unghiurile =>
[tex]\frac{\alpha}{7} = \frac{\beta}{8} = \frac{\gamma}{9} = \frac{\theta}{12} =>\\\alpha = 7k\\\beta = 8k\\\gamma = 9k\\\theta = 12k[/tex]
Un patrulater convex are in total 360 grade.
Formula: [tex]G^{o} = (n-2)180^o[/tex], unde n - numarul de laturi.
Inseamna ca suma unghiurilor este 360 =>
[tex]\alpha + \beta + \gamma + \theta = 360^o\\7k + 8k + 9k + 12k = 360^o\\36k = 360^o\\k = 10^o => \alpha = 70^o, \beta = 80^o, \gamma = 90^o, \theta = 120^o[/tex]
