Answer:a) 5 sides
b) 9 sides
Step-by-step explanation:
a) Since the polygon is a regular polygon, all the interior angles are equal. If one exterior angle is 72 degrees, the interior angle would be
180 - 72 = 108 degrees(sum of the angles on a straight line is 180 degrees)
The sum of the interior angles of a polygon is expressed as
180(n - 2)
Where n represents the number of sides that the polygon has. Since the interior angles are equal, then
108n = 180(n - 2)
108n = 180n - 360
180n - 108n = 360
72n = 360
n = 360/72 = 5
b) If one exterior angle is 40 degrees, the interior angle would be
180 - 40 = 140 degrees
Since the interior angles are equal, then
140n = 180(n - 2)
140n = 180n - 360
180n - 140n = 360
40n = 360
n = 360/40 = 9
