Regular polygon

Question

If the angle at the centre is 18°, how many sides a regular polygon must have to get the angle at the centre to 18°.

Answer 1

All vertices of a regular polygon lie on a common circle, also known as the circumscribed circle. Every circle constitutes 360°. By this, we can determine the angle (α) at the center of any n-sided regular polygon by dividing 360° by the number of sides (n). Conversely, we can determine the number of sides (n) by dividing 360° by the regular angle at the center (α).

360° ÷ n = α ; Conversely, 360° ÷ α = n

360° ÷ 18° = 20 sides