a) Ta có:

AB $\bot$ AC (gt)

AB $\bot$ BD (gt) 

$\Longrightarrow$ AC $//^{}$ BD (dấu hiệu nhận biết hai đường thẳng song song)

Vậy AC $//^{}$ BD

b) Vì AC $//^{}$ BD (gt) $\Longrightarrow$ $\widehat{ACD}$ $+^{}$ $\widehat{BDC}$ $=^{}$ $180^o$ (cặp góc trong cùng phía bù nhau)

$\Longrightarrow$ $135^o$ $+^{}$ $\widehat{BDC}$ $=^{}$ $180^o$ 

$\Longrightarrow$ $\widehat{BDC}$  $=^{}$  $180^o$ $-^{}$ $135^o$ $=^{}$ $45^o$ 
Vậy $\widehat{BDC}$ $=^{}$ $45^o$