Question

A regular polygon is rotated 10° and congruent to the original figure. How many sides does the polygon have?

Answer 1

36 sides

Step-by-step explanation:

For a regular polygon to be rotated by an angle and be congruent to the original figure, the angle of rotation must be equal to the exterior angle of the regular polygon.

For a regular polygon with n sides:

`\begin{gathered} \text{Exterior angle}=(360^0)/(n) \\ S.ince\text{ the angle of rotation is 10 degrees, we have:} \\ \text{10}=(360^0)/(n) \\ 10n=360^0 \\ n=(360)/(10) \\ n=36\text{ sides} \end{gathered}`

The polygon has 36 sides.