I scanned the image with my visual work and I don't know where to go from there.
Any help would be greatly appreciated!
Thanks in advance!
Hello, s3a!
Draw AD.
$\displaystyle \Delta DAC$ is inscribed in a semicircle.
. . Hence: .$\displaystyle \angle DAC = 90^o \quad\Rightarrow\quad \angle DAB = 40^o \quad\Rightarrow\quad \text{arc}(DB) = 80^o \quad\Rightarrow\quad \angle DCB = 40^o$
In $\displaystyle \Delta BEC\!:\;\;\angle BEC + \angle ECB + \angle CBE \:=\:180^o\quad\Rightarrow\quad \angle BEC \;+\; 40^o \;+\; 65^o \;=\;180^o$
Therefore: .$\displaystyle \angle BEC \:=\:75^o$