anviththumma anviththumma
  • 26-03-2018
  • Mathematics
contestada

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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calculista
calculista calculista
  • 04-04-2018
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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