Yes- they are all right angles.
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They can, but usually they are not. All the angles will be equal only if your parallelogram is a rectangle.
A rectangle is a parallelogram in which all four vertex angles equal 90°.
Not unless all angles are also equal. A rhombus is a parallelogram with all sides equal. A rectangle is a parallelogram with all angles equal. A square is a rhombus with all angles equal which is a parallelogram with all sides equal and all angles equal.
A square. * * * * * Or a rectangle.
They can have some (or all) equal angles. A rectangle, for example, has all four angles equal but, because its sides are not the same measure, it is not a regular shape.