Xét `triangle``ICD` có :

$\widehat{CID}$ `+` $\widehat{ICD}$ `+` $\widehat{IDC}$ `=` $180^0$

$\Rightarrow$ $\widehat{ICD}$ `+` $\widehat{IDC}$ `=` $180^0$ `-` $115^0$ `=` $65^0$

$\Rightarrow$ $\frac{1}{2}$  `(` $\widehat{ADC}$ + $\widehat{BCD}$ `)` `=` $65^0$

$\Rightarrow$ $\widehat{ADC}$ `+ ` $\widehat{BCD}$ `=` $130^0$

Xét tứ giác ABCD có :

$\widehat{A}$ `+` $\widehat{B}$ `+` $\widehat{BCD}$ `+` $\widehat{ADC}$ `=` $360^0$

$\Rightarrow$ $\widehat{A}$ `+` $\widehat{B}$ `=` $360^0$ `-` $130^0$ `=` $230^0$

mà $\widehat{A}$ `-`$\widehat{B}$ `=` $50^0$

nên $\widehat{A}$ `=` $\frac{230^0 + 50^0}{2}$  `=` $140^0$

$\widehat{A}$ `-` $\widehat{B}$ `=` $50^0$

$\Rightarrow$ $140^0$ `-` $\widehat{B}$ `=` $50^0$

$\Rightarrow$ $\widehat{B}$`=` $140^0$ ` -`  $50^0$ =  $90^0$