The diagram shows part of a regular polygon. The interior angle and the exterior angle at a vertex are marked. The size of the interior angle is 7 times the size of the exterior angle. Work out the number of sides of the polygon.

Let's have some fun with angles and polygons! In a regular polygon, the interior angle (I) and exterior angle (E) are related as follows: I + E = 180 degrees. You know that I = 7E. Substituting I in the equation gives us 7E + E = 180, or 8E = 180. Solving for E, we get E = 22.5 degrees. The number of sides (n) of a polygon can be found using the exterior angle: E = 360/n. So, 22.5 = 360/n leads us to n = 360/22.5 = 16. Thus, the polygon has 16 sides! Now, here’s a clever nugget: Did you know that the sum of the interior angles of a polygon can also be calculated with the formula (n - 2) × 180? For our 16-sided polygon, this gives (16 - 2) × 180 = 2520 degrees! Just a fun fact to carry in your pocket when discussing polygons with friends or in class!