Yes.
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A rhombus has a pair of opposite equal acute angles and a pair of opposite equal obtuse angles and the four angles add up to 360 degrees.
A rhombus has a pair of equal acute angles opposite one another. The other two angles are supplementary to these and so are also equal.
Any regular polygon with an even number of sides will have diagonals that satisfy this requirement.
Not enough information. Consecutive angles add up to 90 degrees. Opposite angles are congruent and vary depending on how flat the rhombus is.
The opposite angles of a rhombus are congruent so there must be at least two pair of same sized angles. Since a square is a rhombus, we could have all 4 angles of equal size too.