This problem:

1. Find the longer diagonal of a parallelogram whose sides are 12 and 13 cms  if the angle between them is 80 degrees.

makes perfect sense and I can show you how to do that, BUT ONLY
if the problem stops there. 

However, that last part 

2. "and the smallest angle is 35 degrees" 

makes no sense at all, because none of the angles of the parallelogram
defined by 1 have any angle equal to 35 degrees!

So I am going to have to ignore that last part 2, because it is totally
incompatible with the first part 1.

Ignoring 2 completely, we have this parallelogram:

 


Let me know in the thank-you note if this is what you want, because
the 35° part makes no sense.

Edwin