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7 April, 11:50

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°.

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  1. 7 April, 13:10
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    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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