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Q: What shape has 5 lines of symmetry and no right angles?

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A rectangle.

pentagram

A rectangle. Obviously the right angles are in the four corners of the rectangle. The lines of symmetry occur across the horizontal and vertical. There are no lines of symmetry on the diagonal.

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.

A pentagon has five lines of symmetry. It also has five internal angles.

a square

A rectangle.

rhombus

Parrallelogram (it has rotational symmetry but no lines of symmetry)

square and rectangles are technicality squares

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