maximilian26 maximilian26
  • 23-03-2018
  • Mathematics
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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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Blitztiger
Blitztiger Blitztiger
  • 02-04-2018
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.
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