6) How many axes of symmetry does the figure on the side have?

(A) 2

(B) 4

(C) 6

(D) 8

(E) none of the above.

![](https://cdn.mathpix.com/cropped/2024_04_17_548b825896d130d6fc47g-1.jpg?height=317&width=320&top_left_y=248&top_left_x=2406)
6) The answer is (E)

The regular octagon has 8 axes of symmetry, 4 passing through 2 opposite vertices and 4 passing through the midpoints of two opposite sides. The four axes of the first type are not axes of symmetry of the entire figure, because none of the squares constructed on the sides have a symmetric square with respect to these axes. The four axes of the second type are also not axes of symmetry of the entire figure, because the two diagonals of the octagon drawn in the given figure do not have their corresponding symmetrical counterparts. Therefore, there is no axis of symmetry.