Xét ΔDEF có \(\widehat{DEF}+\widehat{DFE}+\widehat{EDF}=180^0\)
=>\(\widehat{DEF}+\widehat{DFE}=180^0-\widehat{EDF}\)
EM là phân giác của góc DEF
=>\(\widehat{DEM}=\widehat{MEF}=\dfrac{\widehat{DEF}}{2}\)
FM là phân giác của góc DFE
=>\(\widehat{DFM}=\widehat{MFE}=\dfrac{\widehat{DFE}}{2}\)
\(\widehat{MEF}+\widehat{MFE}=\dfrac{1}{2}\left(\widehat{DEF}+\widehat{DFE}\right)\)
\(=\dfrac{1}{2}\left(180^0-\widehat{EDF}\right)\)
\(=90^0-\dfrac{1}{2}\cdot\widehat{EDF}\)
Xét ΔEMF có \(\widehat{MEF}+\widehat{MFE}+\widehat{EMF}=180^0\)
=>\(\widehat{EMF}=180^0-\widehat{MEF}-\widehat{MFE}\)
=>\(\widehat{EMF}=180^0-\left(90^0-\dfrac{\widehat{EDF}}{2}\right)\)
\(=180^0-90^0+\dfrac{1}{2}\cdot\widehat{EDF}=90^0+\dfrac{\widehat{EDF}}{2}\)