Explanation:

Step-by-step Solution:

1. Properties of a Rhombus:

   • All sides are equal.
   • The diagonals bisect each other at right angles (90°).
   • The diagonals bisect the angles of the rhombus.

2. Using the Given Information:

   • The given angle at A is 40°.
   • Since the diagonals bisect the angles, each half of angle A is 40° / 2 = 20°.

3. Using the Triangle Rule:
   In triangle ABD, the angles are:  x+20°+90°=180°

4. Solving for x:  x+110°=180°  

                                  x=180°−110°=70°

Conclusion:
The correct value of x is 60°.

Correct Answer: Option D (60°)