Find the measure of each interior angle and each exterior angles of the following regular polygons. Show your work. Decagon Pentagon Dodecagon 16-gon 25-gon
Accepted Solution
A:
Hey there, Decagon - (10 - 2) x 180 degrees = 8 x 180 degrees = 1,440 degrees (sum of angles) 1 angle = 1,440 degrees / 10 = 144 degrees Pentagon - (5 - 2) 180 degrees = 3 x 180 degrees = 540 degrees (sum of angles) 1 angle = 540 degrees / 5 = 108 degrees Do decagon - (12 - 2 ) x 180 degrees = 10 x 180 degrees = 1,800 degrees (sum of angles) 1 angle = 1,800 / 12 = 150 degrees 16 - gon - ( 16 - 2) x 180 degrees = 14 x 180 degrees = 2,520 degrees (Sum of angles) 1 angle = 2,520 degrees / 16 = 157.5 degrees 25 - gon - (25 - 2) x 180 degrees = 23 x 180 degrees = 4,140 degrees (sum of angles) 1 angle = 4,140 / 25 = 165.6 degrees The formula = (n - 2) x 180 degrees