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
To find the number of sides of a regular polygon, we can use the relationships between its interior and exterior angles. Step 1: Define the relationships between interior and exterior angles. Let I be the measure of one interior angle and E be the measure of one exterior angle of a regular polygon. We know that for any polygon, the sum of an interior angle and its corresponding exterior angle is 180^: I + E = 180^ We are given that the interior angle is twice the exterior angle: I = 2E Step 2: Solve for the exterior angle. Substitute the second equation into the first equation: 2E + E = 180^ 3E = 180^ E = (180^)/(3) E = 60^ Step 3: Use the exterior angle to find the number of sides. For a regular polygon with n sides, the measure of one exterior angle is given by the formula: E = (360^)/(n) Substitute the value of E we found: 60^ = (360^)/(n) Now, solve for n: n = (360^)/(60^) n = 6 The number of sides of the regular polygon is 6. Comparing this with the given options: A. 3 B. 8 C. 2 D. 6 The calculated number of sides matches option D. The final answer is D. 6.