Which of the following are possible measures of the exterior angle's of the regular polygon? if the measures are possible, how many sides does the polygon have: 90°, 80°, 75°, 30°, 46°, 36°, 2°.

See below.

Step-by-step explanation:

The sum of the exterior angles of any convex polygon is 360 degrees.

Therefore for a regular polygon n * E = 360 where n = the number of sides in the polygon , n is an integer greater than 2 and E =  value of each exterior angle.

Answers:

Exterior angle = 90,  90 * 4 = 360 so this polygon has 4 sides.

80 degrees:  n * 80 = 360, n = 4.5 so this angle is not possible.

75 degrees:  n * 75 = 360, n = 4.8 so this is not possible.

30 degrees: n * 30 = 360 , n = 12 so this has 12 sides.

46 degrees: n * 46 = 360, n = 7.8 so this is not possible.

36 degrees: n * 36 = 360, n = 10 so this has 12 sides.

2 degrees:  n * 2 = 360, n = 180, so this has 180 sides.

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