\(\Delta BAM\) có BA = BM => \(\Delta BAM\) cân tại B
=> \(\widehat{BAM}=\widehat{BMA}\)
\(\Delta CAN\) có CN = CA => \(\Delta CAN\) cân tại C
=> \(\widehat{CAN}=\widehat{CNA}\)
Suy ra:
\(\left\{{}\begin{matrix}\widehat{AMN}=\dfrac{180^o-\widehat{B}}{2}\\\widehat{ANM}=\dfrac{180^o-\widehat{C}}{2}\end{matrix}\right.\Rightarrow\widehat{AMN}+\widehat{ANM}=\dfrac{180^o-\widehat{B}+180^o-\widehat{C}}{2}=\dfrac{360^o-\left(\widehat{B}+\widehat{C}\right)}{2}=\dfrac{360^o-\left(180^o-90^o\right)}{2}=\dfrac{360^o-90^o}{2}=135^o\)
\(\Rightarrow\widehat{MAN}=180^o-135^o=45^o\)