Find 72 degrees and 40 degrees from the picture

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