Bài 4 :
a) Xét ΔABC có
\(\widehat{A}+\widehat{B}+\widehat{C}=180^o\)
\(\Leftrightarrow\widehat{A}+90^o+\widehat{C}=180^o\Leftrightarrow\widehat{A}+\widehat{C}=180^o\)
Có \(\widehat{A_1}=\widehat{A_2},\widehat{C_1}=\widehat{C_2}\)
\(\Rightarrow\widehat{A_2}+\widehat{C_1}=\dfrac{1}{2}.\left(\widehat{A}+\widehat{C}\right)=45^o\)
Xét ΔAIC có : \(\widehat{A_2}+\widehat{AIC}+\widehat{C_1}=180^o\)
\(\Rightarrow\widehat{AIC}+45^o=180^o\)
\(\Rightarrow\widehat{AIC}=135^o\)
b) Có \(\widehat{ACx}=180^o;\widehat{C_1}=\widehat{C}_2;\widehat{C_3}=\widehat{C_4}\)
\(\Rightarrow\widehat{C_2}+\widehat{C_3}=90^o=\widehat{ICK}\)
Xét ΔICK có góc AIC là góc ngoài Δ
\(\Rightarrow\widehat{AIC}=\widehat{ICK}+\widehat{CKA}\)
\(\Leftrightarrow135^o=90^o+\widehat{CKA}\)
\(\Leftrightarrow\widehat{CKA}=45^o\)
