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
Here's how to solve the problem: a) The number of triangles the polygon can be subdivided into. Step 1: Recall the formula for the sum of interior angles of a polygon. The sum of the interior angles of a polygon with n sides is given by S = (n-2) × 180^. The term (n-2) represents the number of non-overlapping triangles the polygon can be divided into. Step 2: Use the given sum to find the number of triangles. Given that the sum of the interior angles is 1980^. Let T be the number of triangles. T × 180^ = 1980^ T = (1980^)/(180^) T = 11 The number of triangles the polygon can be subdivided into is 11. b) The number of sides the polygon has. Step 3: Relate the number of triangles to the number of sides. The number of triangles a polygon can be subdivided into is n-2, where n is the number of sides. n-2 = T n-2 = 11 n = 11 + 2 n = 13 The number of sides the polygon has is 13. The final answers are: a) The number of triangles the polygon can be subdivided into is 11. b) The number of sides the polygon has is 13. Send me the next one 📸