Question

In a quadrilateral $ABCD$ ; angles $A,B,C$ and $D$ are in the ratio $3:2:1:4$. then $AD$ is parallel to $BC$.
If true then enter $1$ and if false then enter $0$.

Answer 1

$GivenisquadrilateralABCDwithanglesA,B,C\&Dintheratioof3:2:1:4.Nowweknowthatsumofallanglesofaquadrilateral={360}^{o}So\angle A=\frac{3}{10}\times {360}^o={108}^o;\angle B=\frac{2}{10}\times {360}^o={72}^o;\angle C=\frac{1}{10}\times {360}^o={36}^o;\angle D=\frac{4}{10}\times {360}^o={144}^{o}Fromthefigure,\angle A+\angle B={108}^o+{72}^o\Rightarrow \angle A+\angle B={180}^{o}i.e.SumofinterioranglesonthesamesideofthetransversalAB={180}^o\therefore BC\parallel AD.$