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ABCD is a rhombus with diagonals intersecting at E. If m<ABC is three times m<BAD, find m< EBC

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Let m<BAD = x. Then m<ABC = 3x. Since ABCD is a rhombus, AD is parallel to BC and <BAD is an alternate interior angle to < ABC. Thus m<BAD = x = m<EBC.

Therefore, m<EBC = x.
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