Question

Cine poate sa ma ajute!!!!

Answer 1

$\Delta BNC -echilateral \Rightarrow BN =NC. \\ \\ m(\ \textless \ NBC)=m(\ \textless \ NCB)=60 \textdegree \Rightarrow m(\ \textless \ ABN)=m(DCN)=30 \textdegree. \\ \\ BN=CN,~AB=CD,~\ \textless \ ABN \equiv ~\ \textless \ DCN \Rightarrow \Delta ABN \equiv \Delta DCN \\ (LUL). \\ \\ \Rightarrow AN=ND,~deci~\Delta AND -isoscel. \\ \\ BN=CN=AB=CD \Rightarrow \Delta ABN , \Delta DCN-isoscele \Rightarrow \\ \\\Rightarrow m( ABN)=m(\ \textless \ ANB)=m(\ \textless \ DCN)=m(\ \textless \ DNC)= \\ \\ = \frac{180 \textdegree - 30 \textdegree}{2}=75 \textdegree.$

$m(\ \textless \ NAB)=m(\ \textless \ NDC)=75 \textdegree \Rightarrow m(\ \textless \ DAN)=m(\ \textless \ ADN)=15 \textdegree. \\ \\ Rezulta ~ca~M=N.$