The ten-pointed star in the image has six lines of symmetry: one at 180 degrees and five at 36 degrees each. These lines are created by rotational symmetry, where rotating the star by specific angles makes it coincide with itself.
The shape appears to be a ten-pointed star with five outward-facing triangles and five inward-facing triangles.
Here's how to find the lines of symmetry:
Identify rotational symmetry: A line of symmetry is an imaginary line that divides a shape into two equal halves. In the case of a star, rotational symmetry comes into play. If you rotate the star by a certain angle, it will perfectly overlap with itself.
Analyze rotational angles: For a ten-pointed star, there are two main rotational angles that create lines of symmetry:
180 degrees: Rotating the star by 180 degrees will make it flip over itself, creating one line of symmetry that passes through the center of the star.
36 degrees: Rotating the star by 36 degrees five times (a total of 180 degrees) will also make it overlap with itself. This creates five lines of symmetry that pass through the center of the star and bisect the angles between the outward and inward triangles.
Combine rotational symmetries: Therefore, the ten-pointed star in the image has a total of six lines of symmetry:
One line at 180 degrees.
Five lines at 36 degrees each.