How many lines of symmetry are

found in a regular polygon with 40

This is assuming that 40 refers to sides.

Since 40 is an even number, you can have lines of symmetry going from any vertex to the opposite one. Since there can be two identical lines, we just cut in half 40 to 20 so there are no repeats. We can do this for halfway between two vertices as well, so that's another 20. Twenty + 20 = 40 and thus, your answer is 40 lines of symmetry.