Knowing that the tiles are regular polygons, we can deduce that each angle of the tile B is 60. Drawing a circle where a vertex of tile B is the center, we can also deduce that the major angle created by the sides of tile B is 300 because all central angles in a circle add up to 360. Since all A tiles are congruent (they are regular and share the same side), we know that their interior angles are also congruent. Since we know their interior angles add up to 300 (because 2 of their interior angles + 60 = 360), we can divide 300 by 2 to calculate each interior angle, which is 150. By subtracting 150 from 180, we get 30 which is the measure of each EXTERIOR angle of tile A. From basic geometry knowledge, we know that the sum of all exterior angles is 360. Using this, we can divide 360 by 30 to get 10 which is the number of sides of tile A.
Final Answer: Tile A has 10 sides, or in other words is decagon.
