Find the number of diagonals of a regular polygon, sum

Solution

ATQ, Sum of interior angles = [(n - 2) × 180°] We are given that the sum of interior angles is 2700°. So we can set up the equation: [(n - 2) × 180° = 2700°] Now, let's solve for "n": n - 2 = 2700°/180° n - 2 = 15 n = 15 + 2 n = 17 So, the regular polygon has 17 sides. Now, let's find the number of diagonals in a regular polygon with 17 sides.  The formula to calculate the number of diagonals in a regular polygon is given by: Number of diagonals =[ n × (n - 3)/2] Substitute the value of "n" (17) into the formula: Number of diagonals = [17 × (17 - 3)/2] Number of diagonals = 17 × (14/2) Number of diagonals = 119 Therefore, the regular polygon with 17 sides has 119 diagonals.