The angle bisector of ∠ACD in rhombus ABCD makes a 64° angle with the diagonal

BD
. Find the measure of ∠BAD.

3 answers

Huh?

The angle bisector is the diagonal AC.

The diagonals of a rhombus are perpendicular.
Assuming you made a sketch.

Let the angle bisector of ∠ACD meet BD at E
let the diagonals intersect at F

In a rhombus the diagonals right-bisect each other.
So, in triangle CEF, angle F = 90
angle E = 64, thus angle FCE = 26°

which makes angle BCD = 104°
and of course ∠BAD = 104°
nice save, Reiny. I later realized how I had misread the problem.