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A-B-C-and-D-are-angles-of-tetragon-if-A-D-240-C-D-200g-B-D-2pi-3-find-D-




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

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