Question

The angle bisector of ∠ACD in rhombus ABCD makes a 64° angle with the diagonal BD. Find the measure of ∠BAD.

Answer 1

The complete question in the attached figure

we know that
the diagonals of a rhombus intersect to form right angles, 
so
angle ACE is ----------> (90°-64°)-----------> 26° 
ACE is the angle bisector of ACD, this means that ACD is ---------> 26 x 2 = 52°

 The diagonals are angle bisectors to the opposite corners
so 
ACD = ACB = 52° 
and 
BCD = 52 x 2 = 104°
For a rhombus, opposite angles are equivalent,
so 
BAD = BCD = 104°

the answer is 
angle BAD=104°