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: Use the formula for the measure of each interior angle of a regular polygon. The formula for the interior angle of a regular polygon with n sides is given by: Interior Angle = ((n-2) × 180^)/(n) We are given that the interior angle is 175^. Substitute this value into the formula: 175^ = ((n-2) × 180^)/(n) Step 2: Multiply both sides of the equation by n to eliminate the denominator. 175n = (n-2) × 180 Step 3: Distribute 180 on the right side of the equation. 175n = 180n - (2 × 180) 175n = 180n - 360 Step 4: Rearrange the equation to solve for n. Subtract 180n from both sides. 175n - 180n = -360 -5n = -360 Step 5: Divide both sides by -5 to find the value of n. n = (-360)/(-5) n = 72 The number of sides of the polygon is 72. The number of sides of the polygon is 72. That's 2 down. 3 left today — send the next one.