Find the number of sides in a regular polygon if each interior angle is 160°.

Explanation

Given: Each interior angle of a regular polygon is 160°. To Find: The number of sides of the polygon (denoted as n). Step-by-Step Solution For a regular polygon with n sides, the measure of each interior angle is given by the formula: Interior Angle = ( (n - 2) × 180° ) / n We are given that each interior angle is 160°, so: 160 = ( (n - 2) × 180 ) / n Step 1: Cross Multiply 160n = (n - 2) × 180 Step 2: Expand and Simplify 160n = 180n - 360 Move 160n to the right side: 0 = 20n - 360 Step 3: Solve for n 20n = 360 n = 360 / 20 n = 18 Final Answer The number of sides in the regular polygon is 18.