Xét $\Delta $ ABH có:

$\widehat{BAH}+\widehat{AHB}+\widehat{B}={{180}^{0}}$

$\Rightarrow \widehat{B}={{180}^{0}}-(\widehat{BAH}+\widehat{AHB})$

$\Rightarrow \widehat{B}={{180}^{0}}-({{45}^{0}}+{{90}^{0}})={{45}^{0}}$

Xét $\Delta $ABC có:

$\widehat{A}+\widehat{B}+\widehat{C}={{180}^{0}}$

$\Rightarrow \widehat{C}={{180}^{0}}-(\widehat{A}+\widehat{B})$

$\Rightarrow \widehat{C}={{180}^{0}}-({{90}^{0}}+{{45}^{0}})$

$\Rightarrow \widehat{C}={{45}^{0}}$