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Triangle AOB Triangle OAD are congruent triangles
Thereforeangle OAB= Angle OAD
Angle OAB=55 deg (given)
Then Angle OAD = 55 deg
Angle BAD = 55+55 = 110 deg
Again angle OBA + angle OAB + angle BOA = 180 deg
But angle OAB = 55 angle BOA = 90 (Diagonals are perpendicular bisector)
Therefore angle OBA = 180-90-55 = 35 deg
But angle OBA= angle OBC = 35 deg
Therefore angle ABC = 35+35 =70 deg
Opposite angles in rhombus are equal
Therefore angles of rhombus ABCD are 110, 70, 110 70 (Answer
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