SOLUTION: Hello Tutors, I am having trouble with this problem: The angle bisector of angle-ACD in rhombus ABCD makes a 64 degree angle with the diagonal BD. Find the measure of angle-B

Question 858350: Hello Tutors,
I am having trouble with this problem:
The angle bisector of angle-ACD in rhombus ABCD makes a 64 degree angle with the diagonal BD. Find the measure of angle-BAD.
Would you know how to draw this rhombus and how to label each corner? I don't know what the order of ABCD is in this rhombus that will actually make sense.
Thank you!
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
angle ACD and a diagonal of BD are inconsistent with each other.
If BD is a diagonal, then AC has to be the other diagonal.
If AC is the other diagonal, then angle ACD is impossible.
you could have angle ADC or ABC or DAB or DCB, but you can't have angle ACD.
If i assume the angle is ADC, then the problem makes more sense.
in that case, the bisector of angle ADC should be the diagonal BD.
this means angle ADC is 128 degrees which means that angle BAD is equal to 52 degrees.
the properties of a rhombus are shown in the following reference:
http://www.wyzant.com/resources/lessons/math/geometry/quadrilaterals/rectangles_rhombuses_squares
one of those properties is that the diagonals of the rhombus bisect the opposite the angles they are connected to.
a picture of your rhombus, will more then likely look like this:
$$$

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