Question

part c
how can you use the measures of arcs created by an inscribed regular polygon to determine the rotations that will map the polygon onto itself?
show hints
divide 90 by the number of arcs.
divide 270 by the number of arcs.
divide 360 by the number of arcs.
divide 180 by the number of arcs.

Explanation:

Step1: Recall rotational symmetry concept

A full - rotation is 360°. For a regular polygon inscribed in a circle, the angles of rotation that map the polygon onto itself are the angles by which we can rotate the polygon around its center so that it looks the same as before the rotation. The number of distinct rotational symmetries of a regular polygon is equal to the number of its sides (which is equal to the number of arcs created by the vertices of the inscribed polygon on the circum - circle).

Step2: Determine the rotation angle formula

To find the smallest non - zero angle of rotation that maps a regular polygon onto itself, we divide the full - rotation angle (360°) by the number of sides (or the number of arcs). This gives us the angle of rotation for each "step" of symmetry.

Answer:

Divide 360 by the number of arcs.