$a)$

Vì $\text{ABCD}$ là hình bình hành nên:

$\widehat{\text{C}}=\widehat{\text{A}}=100^\circ$

$\widehat{\text{A}}+\widehat{\text{B}}=180^\circ$

$\Rightarrow\widehat{\text{B}}=180^\circ-\widehat{\text{A}}=180^\circ-100^\circ=80^\circ$

$\Rightarrow\widehat{\text{D}}=\widehat{\text{B}}=80^\circ$

Vậy $\widehat{\text{A}}=\widehat{\text{C}}=100^\circ,\widehat{\text{B}}=\widehat{\text{D}}=80^\circ$

$b)$

Vì $\text{ABCD}$ là hình bình hành nên:

$\widehat{\text{A}}+\widehat{\text{B}}=180^\circ$

Mà $\widehat{\text{A}}-\widehat{\text{B}}=20^\circ$ nên:

$\widehat{\text{A}}=\dfrac{180^\circ+20^\circ}{2}=100^\circ$

$\widehat{\text{B}}=180^\circ-100^\circ=80^\circ$

$\widehat{\text{C}}=\widehat{\text{A}}=100^\circ$

$\widehat{\text{D}}=\widehat{\text{B}}=80^\circ$

Vậy $\widehat{\text{A}}=\widehat{\text{C}}=100^\circ,\widehat{\text{B}}=\widehat{\text{D}}=80^\circ$