This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
The size of each exterior angle of the polygon is 40°. Steps: 1. Find the number of sides (n) of the polygon. The formula for the sum of the interior angles of a polygon is (n - 2) * 180°. Given the sum is 1260°: (n - 2) * 180° = 1260° n - 2 = 1260 / 180 n - 2 = 7 n = 7 + 2 n = 9 The polygon has 9 sides (it's a nonagon). 2. Calculate the size of each exterior angle. For any regular polygon, the sum of its exterior angles is 360°. Since it's a regular polygon, all exterior angles are equal. Each exterior angle = Sum of exterior angles / n Each exterior angle = 360° / 9 Each exterior angle = 40°