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
Fresh day Mallam, let's solve. The formula for the sum of the interior angles of a polygon with n sides is given by S = (n-2) × 180^. a) Find the sum of the interior angles of a regular polygon with 6 sides. Step 1: Identify the number of sides, n. For a polygon with 6 sides, n=6. Step 2: Substitute n into the formula for the sum of interior angles. S = (6-2) × 180^ S = 4 × 180^ S = 720^ The sum of the interior angles is 720^ b) A polygon has 10 sides. Find the sum of interior angles. Step 1: Identify the number of sides, n. For a polygon with 10 sides, n=10. Step 2: Substitute n into the formula for the sum of interior angles. S = (10-2) × 180^ S = 8 × 180^ S = 1440^ The sum of the interior angles is 1440^ c) If the sum of interior angles of a regular polygon is 540^, find the number of sides. Step 1: Set the sum of interior angles formula equal to the given sum. (n-2) × 180^ = 540^ Step 2: Divide both sides by 180^. n-2 = (540^)/(180^) n-2 = 3 Step 3: Solve for n. n = 3 + 2 n = 5 The number of sides is 5 Send me the next one 📸