Most shapes have no right angles.
Circle, pentagon, hexagon etc.
Ones that do include the square and some triangles.
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square
An irregular pentagon can have 5 vertices and two right-angles.
yes, shapes with four right angel are like square, rectangle, rhombus and trapezoid.
I will rephrase your question as "What shape has only three right angles?" A shape is a 2D drawing that encloses some space. The sum of the angles must exceed 270 degrees. A rectangle is out of the question as it has four right angles. But a 5 sided shape with unequal sides (irregular pentagon) or higher number of sides is fine. I wish Wikipedia would let draw on these answers, because I could draw hundreds of shapes with three right angles. When we talk of shapes, the most regular shapes come to mind, triangles, squares, pentagons, etc. But you did not spcify that my shape had to have straight sides. Imagine, for example, a circle which I will break at three places and insert right angles. Weird, but it does have three right angles. Do the right angles have to face in towards the center? I could even draw a more bizarre shape with with three right angles facing out, connected by curved lines.
Oh honey, we're talking about rectangles here. They're like the cool kids of the quadrilateral world with their four sides and two right angles. So next time you see a shape with those specs, just remember it's a rectangle strutting its stuff.