( Hình chỉ mang tính chất hư cấu :v )
Vì AH là phân giác \(\widehat{CAB}\)nên \(\widehat{BAD}=\frac{\widehat{CAB}}{2}=\frac{80^o}{2}=40^o\)
Xét \(\Delta ABC:\)
\(\widehat{CAB}+\widehat{ABC}+\widehat{ACB}=180^o\)( Tổng ba góc trong tam giác )
\(\Rightarrow\widehat{ABC}+80^o+60^o=180^o\)
\(\Rightarrow\widehat{ABC}=40^o\)
\(\Rightarrow\widehat{ABD}=40^o\)( Do \(D\in BC\))
Xét \(\Delta ABD:\)
\(\widehat{ABD}+\widehat{ADB}+\widehat{BAD}=180^o\)(Tổng ba góc trong tam giác )
\(\Rightarrow\widehat{ADB}+40^o+40^o=180^o\)
\(\Rightarrow\widehat{ADB}=100^o\)
Xét \(\Delta HAD\)có \(\widehat{ADB}\)là góc ngoài đỉnh \(D\)
\(\Rightarrow\widehat{HAD}+\widehat{AHD}=\widehat{ADB}=100^o\)
\(\Rightarrow\widehat{HAD}+90^o=100^o\)
\(\Rightarrow\widehat{HAD}=10^o\)
Vậy ...
