Ta có :  AB // CD 

=> $\widehat{A}+\widehat{D}=180^{\circ}$   ( góc trong cùng phía )

Theo gt : $\widehat{A}-\widehat{D}=20^{\circ}$

=> $\widehat{A}=\widehat{D}+20^{\circ}$    (*)

=>  $\widehat{D}+\widehat{D}+20^{\circ}=180^{\circ}$ 

=>  $2\widehat{D}=160^{\circ}$ 

=> $\widehat{D}=80^{\circ}$ 

Thay vào (*)  =>  $\widehat{A}=100^{\circ}$ 

Ta có : $\widehat{B}=2\widehat{C}$ , $\widehat{B}+\widehat{C}=180^{\circ}$ 

=>  $2\widehat{C}+\widehat{C}=180^{\circ}$ 

=>  $\widehat{C}=60^{\circ}$ 

=>  $\widehat{B}=120^{\circ}$ 

Vậy $\left\{\begin{matrix}\widehat{D}=100^{\circ}  &  &  & \\ \widehat{B}=120^{\circ}  &  &  & \\ \widehat{C}=60^{\circ}  &  &  & \\ \widehat{D}=80^{\circ}  &  &  & \end{matrix}\right.$