the third tile. All three tiles types have the same side length. Determine the shape of the third tile type.
Where 3 tiles meet, they must add up to a full 360°. The formula for the interior angle of a regular n-sided polygon is: ((n - 2)*180) / n Plugging in n=4, the interior angle of a square is 90° Plugging in n=5, the angle of a pentagon is 108° The angle of the third tile is x and the 3 angles must add up to a full 360°: 90 + 108 + x = 360 Solve for x: x = 360 - 198 x = 162 Plug that into the original equation and solve for n: ((n - 2) * 180) / n = 162 (n-2) * 180 = 162n n - 2 = (162/180)n n - (162/180)n = 2 (18/180)n = 2 (1/10)n = 2 n = 2 * 10 n = 20 So the third tile must be from a regular icosagon (20-sided polygon) Answer: Regular icosagon; see the picture below.
