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

Mathematics

1 answer:

saveliy_v [14]3 years ago

3 0

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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