# geometry

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

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1. Huh?

The angle bisector is the diagonal AC.

The diagonals of a rhombus are perpendicular.

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2. 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°

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3. nice save, Reiny. I later realized how I had misread the problem.

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