Question

Va rog ajutati-ma!!!!!!!!

Answer 1

$Notam \ cu \ a \ masura \ unghiului \ A , \ respectiv \ b, \ c, \ d, \ masurile \ unghiurilor \ B, \ C, \ D \\ \\ \frac{a}{4} = \frac{b}{5} = \frac{c}{6} = k \\ \\ \frac{c}{14} = \frac{d}{5} \\ \frac{c}{6} : \frac{c}{14} = \frac{ \frac{c}{6} } { \frac{c}{14} } = \frac{c}{6} * \frac{14}{c} = \frac{14}{6} \Rightarrow \frac{c}{14} = \frac{c}{6} * \frac{6}{14} \\ \\ \frac{a}{4} = k \Rightarrow a= 4k \\ \frac{b}{5} = k \Rightarrow b = 5k \\ \frac{c}{6} = k \Rightarrow c = 6k \\ \frac{c}{6} * \frac{6}{14} = \frac{6k}{14} = \frac{3k}{7} \\ \frac{3k}{7} = \frac{d}{5} \Rightarrow d={15k}{7} \\ a + b + c + d = 360 \Rightarrow 4k + 5k + 6k + \frac{15k} {7} = 360 \Rightarrow 15k + \frac{15k} {7} = 360 \Rightarrow \frac{15k*7 + 15k}{7} = 360 \Rightarrow {15k*8} {7} = 360 \Rightarrow k = \frac{ 5*72 * 7}{5*3*8} \Rightarrow k = \frac{ 9*7}{3} \Rightarrow k = 21 \\ a = 4*21 = 84 ; \ b = 5*21 = 105 ; \ c = 6*21 = 126 ; \ d = \frac {15* 21}{7} = \frac {15*3}{1} = 45$