Doug C. answered • 09/24/23
Math Tutor with Reputation to make difficult concepts understandable
A regular pentagon has 5 equal sides and 5 equal internal angles. There are also 5 vertices. If you pick one vertex and picture drawing diagonals to each non-adjacent vertex, 3 triangles will be created. Each triangle contains 180 degrees, so the internal angles of a regular pentagon sum to 3(180) or 540 degrees,
Since each of the 5 angles is equal, divide 540 by 5 to determine the measure of each angle.
In general if a regular polygon contains n sides, then the sum of its internal angles is 180(n-2). Divide that by n to determine the measure of one internal angle. Apply that formula to get the measures of each internal angle for a regular [hexagon has 6 equal angles/sides, and octagon has 8 equal angles/sides].
