Question Number 194931 by sonukgindia last updated on 20/Jul/23
Answered by HeferH last updated on 20/Jul/23
Commented by HeferH last updated on 20/Jul/23
$$\mathrm{6}{x}\:=\:\mathrm{2}\left(\mathrm{180}°−\mathrm{7}{x}\right) \\ $$$$\:\mathrm{3}{x}\:=\:\mathrm{180}°−\mathrm{7}{x} \\ $$$$\:\mathrm{10}{x}\:=\:\mathrm{180}° \\ $$$$\:{x}\:=\:\mathrm{18}°\: \\ $$
Answered by MM42 last updated on 20/Jul/23
$${B}=\mathrm{180}−\mathrm{7}{x}\:\:\&\:\:{D}=\mathrm{180}−\mathrm{6}{x} \\ $$$$\frac{{AB}}{{sin}\mathrm{3}{x}}=\frac{{AC}}{{sin}\mathrm{7}{x}}\:\:\:\&\:\:\frac{{AB}}{{sin}\mathrm{4}{x}}=\frac{{AC}}{{sin}\mathrm{6}{x}} \\ $$$$\Rightarrow{sin}\mathrm{3}{x}×{sin}\mathrm{6}{x}={sin}\mathrm{7}{x}×{si}\mathrm{4}{x} \\ $$$$\Rightarrow{cos}\mathrm{11}{x}={cos}\mathrm{9}{x}\Rightarrow{x}=\frac{\pi}{\mathrm{10}}=\mathrm{18}\:\checkmark \\ $$$$ \\ $$