Question

How many lines of symmetry does a regular decagon have?

Answer 1

`10` in the plane, `11` if you count the perpendicular axis through the centre.

Explanation:

A regular decagon has `5` lines of symmetry that go through opposite vertices and `5` lines of symmetry that go through the midpoints of opposite sides.

There is also a line of symmetry perpendicular to the plane that passes through the centre of the decagon.

Answer 2

Regular figures: The number of sides is the same as the number of lines of symmetry and the order of rotational symmetry.

Explanation:

Regular figures are really easy to work with because their sides and angles are all equal.

The number of sides is always the same as the number of lines of symmetry and the same as the order of rotational symmetry

If there is an EVEN number of sides, then the lines of symmetry run though the midpoints of opposite sides and through opposite vertices.

If there is an ODD number of sides, each line of symmetry will run from one vertex through the midpoint of the opposite side.

Equilateral triangle: `rarr` 3 sides, 3 lines of symmetry
Square:`rarr` 4 sides, 4 lines of symmetry
Regular pentagon:`rarr` 5 sides, 5 lines of symmetry
Regular Hexagon:`rarr` 6 sides, 6 lines of symmetry

and so on .....