Question

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

Answer 1

Since the diagonals of a rhombus intersect to form right angles, this means that angle ACE is 26 degrees. Since CE is the angle bisector of ACD, this means that ACD is 26 x 2 = 52 degrees. The diagonals are angle bisectors to the opposite corners, so ACD = ACB = 52 degrees, and BCD = 52 x 2 = 104 degrees. For a rhombus, opposite angles are equivalent, so BAD = BCD = 104 degrees.