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The equation for the size of an interior angle of an n-sided regular polygon is (n-2)180/n. When n=7, the interior angle of a regular sided shape would be 5x180/7 or approximately 128.57. The polygon in the question has an interior right angle (90 degree angle) and thus cannot be a regular shape. A 7 sided shape is called a heptagon. Thus, the shape described in the question is an irregular heptagon.
A Square
a square...
There are lots of polygons like that. If by 1 right angle, you mean exactly 1 right angle, there are no such quadrilaterals, but there are pentagons (in fact n-gons for all n>=5.)
Not necessarily. A triangle with two equal sides is called an isoceles triangle. A right triangle has one angle that measures 90 degrees.