Alright sanjeet, I spent way more time than I should have to make this fancy for you (about half an hour) but attached below the image is the code.
It determined that the angle is 23.1 degrees. If you want the lines overlaid on the image, I'm sure you can figure out that simple part. As I mentioned in the comments you might want to figure out an algorithm to examine the widths plot and figure out where to fit your line over. The min is fairly straight forward, but the widest part is somewhat of a judgement call.