The angle bisector of ∠acd in rhombus abcd makes a 64° angle with the diagonal bd . find the measure of ∠bad.

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°

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