In December I did the https://www.mscroggs.co.uk/ calendar, solving a daily puzzle.

In January I will present my solutions.

Solution below.

Reveal solution by highlighting:

A polygon with 3 sides (a triangle) has the angle sum 180°. In a regular version each angle will be 180°/3 = 60°.

Every time this polygon “grows” a side, it also “grows” 180° in angle sum. With 4 sides, the sum is 360° and each angle is 360°/4 = 90°.

With n sides, the angle sum is (n-2)*180°. (3 sides: 1*180. 4 sides: 2*180.) And each angle is (n-2)*180°/n.

(n-2)*180°/n = 178°.

(n-2)/n = 178/180.

n = 180.

(Just to be sure: Throw in a sanity check, n shouldn’t be 0 or less.)