octagon
The shape you are describing is a trapezoid. A trapezoid is a quadrilateral with at least one pair of parallel sides. It can have two right angles, but it does not have any lines of symmetry due to its asymmetrical nature.
It is a trapezoid and its other 2 angles are obtuse and acute
The shape that has no lines of symmetry and rotational symmetry order 4 is a scalene triangle. A scalene triangle is a triangle with three unequal sides and three unequal angles. It does not have any lines of symmetry because its sides and angles are not equal, and it has rotational symmetry of order 4 because it looks the same after being rotated by 90, 180, or 270 degrees.
an equilateral triangle
a pentagon
Well, isn't that just a delightful shape you've described! A figure with 5 lines of symmetry and no right angles is called a pentagon. It has those lovely symmetrical qualities that make it so pleasing to the eye. Just imagine all the wonderful ways you could paint and create with such a shape!
A rectangle.
A pentagon has 5 lines of symmetry and no right angle.
octagon
If your asking what shape has three lines of symmetry, your answer would be an equilateral triangle. You can tell how many lines of symmetry a shape that has all angles of the same measure has by looking at it's angles. Ex., pentagon has five angles--five lines of symmetry; octagon has eight angles, eight lines of symmetry; etc.
An irregular quadrilateral.
rhombus
A rectangle.
a square
The shape you are describing is a trapezoid. A trapezoid is a quadrilateral with at least one pair of parallel sides. It can have two right angles, but it does not have any lines of symmetry due to its asymmetrical nature.
Parrallelogram (it has rotational symmetry but no lines of symmetry)