Question Number 126148 by Study last updated on 17/Dec/20
$${A},{B},{C}\:{and}\:{D}\:{are}\:{angles}\:{of}\:{tetragon} \\ $$$${if}\:{A}+{D}=\mathrm{240}^{°\:} \:,\:\:\:{C}+{D}=\mathrm{200}{g} \\ $$$${B}+{D}=\frac{\mathrm{2}\pi}{\mathrm{3}}\:\:\:,\:{find}\:{D}=??? \\ $$
Answered by mahdipoor last updated on 17/Dec/20
$${A}+{B}+{C}+{D}=\mathrm{360}^{°} \\ $$$${A}+{D}=\mathrm{240}^{°} \\ $$$${C}+{D}=\mathrm{200}{g}×\frac{\mathrm{360}^{°} }{\mathrm{400}{g}}=\mathrm{180}^{°} \\ $$$${B}+{D}=\frac{\mathrm{2}\pi}{\mathrm{3}}{rad}×\frac{\mathrm{360}^{°} }{\mathrm{2}\pi\:{rad}}=\mathrm{120}^{°} \\ $$$$\Rightarrow{D}=\mathrm{90},{B}=\mathrm{30},{C}=\mathrm{90},{A}=\mathrm{150} \\ $$