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: Let the interior angle be I and the exterior angle be E. The problem states that the ratio of the interior angle to the exterior angle is 5:2. (I)/(E) = (5)/(2) This means I = (5)/(2)E. Step 2: The sum of an interior angle and its corresponding exterior angle of any polygon is 180^. I + E = 180^ Substitute the expression for I from Step 1 into this equation: (5)/(2)E + E = 180^ (5)/(2)E + (2)/(2)E = 180^ (7)/(2)E = 180^ Step 3: Solve for the exterior angle E. E = (180^ × 2)/(7) E = (360^)/(7) Step 4: For a regular polygon with n sides, the measure of each exterior angle is given by the formula: E = (360^)/(n) Now, equate the value of E found in Step 3 with this formula: (360^)/(7) = (360^)/(n) Step 5: Solve for n, the number of sides of the polygon. n = 7 The number of sides of the polygon is 7. The number of sides of the polygon is 7. Send me the next one 📸