Any angle can be bisected using a compass and a straight edge.
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No. The biggest possible obtuse angle is one that's a hair less than 180 degrees. Bisect that, and each half is the biggest possible ACUTE angle.
45 degrees * * * * * The diagonals of a rectange bisect one another but can do so at any angle, x, such that 0<x<180 degrees.
no
Yes
A diagonal always forms an angle bisector in a square. In a rectangle, trapezoid, or any other quadrilateral, a diagonal does not always bisect the angles.