Bài này vẽ tượng trưng thôi cx đc nhé, vì mới vô không biết chính xác góc nào bao nhiêu độ....

`a)`
Ta có:
$\widehat{A} + \widehat{B} + \widehat{C} + \widehat{D} = 360^\circ$ (1)
$\widehat{B} + \widehat{C} = 200^\circ$ (2)
$\widehat{B} + \widehat{D} = 180^\circ$ (3)
$\widehat{C} + \widehat{D} = 120^\circ$ (4)
`-`
$(2) + (3) + (4) \Rightarrow 2(\widehat{B} + \widehat{C} + \widehat{D}) = 200^\circ + 180^\circ + 120^\circ = 500^\circ$
$\Rightarrow \widehat{B} + \widehat{C} + \widehat{D} = 250^\circ$ (5)

`-`
$(1) \Leftrightarrow \widehat{A} + (\widehat{B} + \widehat{C} + \widehat{D}) = 360^\circ$
$\Leftrightarrow \widehat{A} + 250^\circ = 360^\circ \Leftrightarrow \widehat{A} = 110^\circ$.
`-`
Từ (5) và (3) $\Rightarrow \widehat{C} = (\widehat{B} + \widehat{C} + \widehat{D}) - (\widehat{B} + \widehat{D}) = 250^\circ - 180^\circ = 70^\circ$.
Từ (2) $\Rightarrow \widehat{B} = 200^\circ - \widehat{C} = 200^\circ - 70^\circ = 130^\circ$.
Từ (4) $\Rightarrow \widehat{D} = 120^\circ - \widehat{C} = 120^\circ - 70^\circ = 50^\circ$.
Vậy $\widehat{A}=110^\circ, \widehat{B}=130^\circ, \widehat{C}=70^\circ, \widehat{D}=50^\circ$.

`b)`
$AI$ là phân giác $\widehat{A} \Rightarrow \widehat{IAB} = \frac{\widehat{A}}{2}$.
$BI$ là phân giác $\widehat{B} \Rightarrow \widehat{IBA} = \frac{\widehat{B}}{2}$.
Trong $\triangle AIB$:
$\widehat{AIB} = 180^\circ - (\widehat{IAB} + \widehat{IBA})$
$\widehat{AIB} = 180^\circ - \left(\frac{\widehat{A}}{2} + \frac{\widehat{B}}{2}\right)$
$\widehat{AIB} = 180^\circ - \frac{\widehat{A} + \widehat{B}}{2}$
`-`
Vì $\widehat{A} + \widehat{B} + \widehat{C} + \widehat{D} = 360^\circ$
$\Rightarrow \widehat{A} + \widehat{B} = 360^\circ - (\widehat{C} + \widehat{D})$
`-`
$\widehat{AIB} = 180^\circ - \frac{360^\circ - (\widehat{C} + \widehat{D})}{2}$
$\widehat{AIB} = 180^\circ - \left(180^\circ - \frac{\widehat{C} + \widehat{D}}{2}\right)$
$\widehat{AIB} = 180^\circ - 180^\circ + \frac{\widehat{C} + \widehat{D}}{2}$
$\widehat{AIB} = \frac{\widehat{C} + \widehat{D}}{2}$.