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
Step 1: Use the formula for the exterior angle of a regular polygon. The measure of an exterior angle of a regular polygon is given by the formula: Exterior\; Angle = (360^)/(n) where n is the number of sides of the polygon. Step 2: Substitute the given exterior angle into the formula. We are given that the exterior angle is 72^. 72^ = (360^)/(n) Step 3: Solve for n. Multiply both sides by n: 72n = 360 Divide both sides by 72: n = (360)/(72) n = 5 The number of sides of the regular polygon is 5. What's next?