Question

The quadrilateral ABCD is a rhombus with BD = BC. On the side

Answer 1

The halves of the rhombus separated by line BD are equilateral triangles.
  ∠BAD = 60°
so
  ∠ADM is 0.80*60° = 48°.

∠BMD is an exterior angle to ΔAMD, so is equal to the sum
  ∠BMD = ∠BAD + ∠ADM
  = 60° +48° = 108°

∠BMD = 108°