Đáp án: $120^o$
Giải thích các bước giải:
Ta có $AH\perp BC, CD\perp AB, AH\cap CD=I$
$\to I$ là trực tâm $\Delta ABC$
$\to BI\perp AC$
Gọi $BI\cap AC=E$
$\to BE\perp AC$
$\to \widehat{AIB}=\widehat{EIH}$
$\to \widehat{AIB}=\widehat{EIC}+\widehat{HIC}$
$\to \widehat{AIB}=(90^o-\widehat{ECI})+(90^o-\widehat{HCI})$
$\to \widehat{AIB}=90^o-\widehat{ECI}+90^o-\widehat{HCI}$
$\to \widehat{AIB}=180^o-(\widehat{ECI}+\widehat{HCI})$
$\to \widehat{AIB}=180^o-\widehat{ECH}$
$\to \widehat{AIB}=180^o-\widehat{C}$
$\to \widehat{AIB}=180^o-60^o$
$\to \widehat{AIB}=120^o$
