lots of shapes are like that! any shape with smooth edges can have no right angles if you rearange the sides and their lengths. a hexagon is any shape with six sides, so it can have almost any angle in it. same with octagon and eight. in fact, shape names are just categories.
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There is no polygonal shape which has exactly those angles. It is possible for a concave polygon with 6 or more vertices to have the given angles.
a shape with 7 vertices
A square, rectangle.
Depends on the shape. A right triangle has one right angle, a rectangle has 4, an equilateral triangle has none, a circle has no angles. There are polygons with more than 4 right angles, and there is no limit on how many, but those with more than 4 are not convex.
The number of vertices does not determine the number of faces. If the shape with 6 vertices was a quadrilateral based bipyramid, it would have 8 faces. A hexagonal based pyramid has 7 vertices and 7 faces. So more vertices does not necessarily imply more faces.