Có MP//AH, AH $\bot$ BC
=> MP $\bot$ BC
=> $\widehat{PMB}= 90^o$
$\Delta$ PMB, $\widehat{PMB}= 90^o$ có $\widehat{BPM}= 90^o- \widehat{PBM}$
$\Delta$ QMC, $\widehat{QMC}= 90^o$ có $\widehat{PQA}= 90^o- \widehat{QCM}$
Mà $\Delta$ ABC cân A => $\widehat{PBM}= \widehat{QCM}$
=> $\widehat{BPM}= \widehat{PQA}$
=> $\widehat{QPA}= \widehat{PQA}$ (đối đỉnh)
=> $\Delta$ APQ cân A
Có $\widehat{ABC}= 50^o$
=> $\widehat{BAC}= 180^o - 2.50^o= 80^o$
=> $\widehat{QAP}= 180-80= 100^o$
=> $\widehat{AQP}= \widehat{APQ}= \frac{180-100}{2}= 40^o$