The quadrilateral abcd is a rhombus with bd = bc. on the side ab a point m is taken so that the measure of ∠adm is 20% smaller than the measure of ∠bad. find the measure of ∠bmd.

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°

Don’t worry about it