We may as well let half the horizontal diagonal be 1 unit and half the
vertical diagonal be y units. Then the horizontal diagonal is 2 and the
vertical diagonal will be 2y units.



The length of one diagonal of a rhombus is a geometric mean of the length of
the other diagonal and the length of the side.

So one diagonal is the square root of the product of the other diagonal and
a side.  So


Square both sides:





y isn't 0, so we divide both sides by 2



Square both sides again







 

 



 

Take the + value so y will be a real number











θ is half the angle on the right.

So the angle on the right (and on the left) is 77.33656498o.

The angle at the top (and at the bottom) is its supplement, so we subtract
that from 180o and get 102.663435o.

Edwin