Question

find the degree and radian measure of exterior and interior angle of a regular Pentagon,hexagon,septagon, octagon​

Answer 1

Answer:

Step-by-step formula of interior angle of regular polygon is  where n is number of sides of polygon.

and then, exterior angle = 180° - interior angle

relation between degree and radian ,

C/π = D/180°

for regular pentagon:

interior angle = (5 - 2) × 180°/5 = 108° or 3π/5

exterior angle = 180° - 108° = 72° or , 2π/5

for regular hexagon :

interior angle = (6 - 2) × 180°/6 = 120° or 2π/3

exterior angle = 180° - 120° = 60° or, π/3

for regular septagon :

interior angle = (7 - 2) × 180°/7 = 900°/7 or, 5π/7

exterior angle = 180° - 900°/7 = 360°/7 or 2π/7

for regular octagon :

interior angle = (8 - 2) × 180°/8 = 135° or, 3π/4

exterior angle = 180° - 135° = 45° or , π/4

explanation: