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
Hey martinodok — ready when you are. Here are the solutions to the questions: Question 7(a): A regular polygon of n sides is such that each interior angle is 120^ greater than the exterior angle. Find: (i) the value of n; (ii) the sum of all the interior angles. Part (i): The value of n Step 1: Define interior and exterior angles. Let the interior angle be I and the exterior angle be E. We know that the sum of an interior angle and its corresponding exterior angle is 180^: I + E = 180^ We are given that the interior angle is 120^ greater than the exterior angle: I = E + 120^ Step 2: Solve for the exterior angle E. Substitute the second equation into the first: (E + 120^) + E = 180^ 2E + 120^ = 180^ 2E = 180^ - 120^ 2E = 60^ E = (60^)/(2) E = 30^ Step 3: Calculate the number of sides n. For a regular polygon