Directions: Fill in all blank spaces in the table. Show all work below the table or on a separate sheet of paper. If needed, round your answer to the nearest tenth.

Answer:

# of sides [tex]{}[/tex]  Interior               One Interior Angle  Exterior           One

           [tex]{}[/tex]        Angle Sum                                          Angle Sum     Exterior Angle

14   [tex]{}[/tex]              2,160°                 154.3°                            360°           25.714°    

24    [tex]{}[/tex]            3,960°                165°                                360°            15°

8    [tex]{}[/tex]               1,080                 135°                                360°            45°

30    [tex]{}[/tex]            5,040                 168°                                360°            12°

12    [tex]{}[/tex]             1,800                  150°                                360°            30°

Step-by-step explanation:

Please find attached the table of values calculated with Microsoft Excel

From the given table, we have the formula for the following parameters;

Number of sides = n

Interior Angle Sum = 180×(n - 2)

Measure of ONE Interior = 180×(n - 2)/n        

Angle (regular polygon)  

Exterior Angle Sum = 360°

Measure of ONE Exterior = 360°/n

Angle (regular polygon)

1) When n = 14, we have;

The interior Angle Sum = 180×(14 - 2) = 2,160°

The measure of one Interior angle (regular polygon) ;  180×(14 - 2)/14 ≈ 154.3°

The exterior angle sum = 360°

The measure of one exterior angle (regular polygon) = 360°/14 ≈ 25.714°

2) When n = 24, we have;

The interior Angle Sum = 180×(24 - 2) = 3,960°

The measure of one interior angle (regular polygon);  180×(24 - 2)/24 = 165°

The exterior angle sum = 360°

The measure of one exterior angle (regular polygon) = 360°/24 = 15°

3) When the interior angle sum = 180×(n - 2) = 1,080°, we have;

n = 1,080°/180° + 2 = 8

n = 8

The measure of one interior angle (regular polygon);  180×(8 - 2)/8 = 135°

The exterior angle sum = 360°

The measure of one exterior angle (regular polygon) = 360°/8 = 45°

4) When the interior angle sum = 180×(n - 2) = 5,040°

n = 5,040°/180° + 2 = 30

n = 30

The measure of one interior angle (regular polygon);  180×(30 - 2)/30 = 168°

The exterior angle sum = 360°

The measure of one exterior angle (regular polygon) = 360°/30 = 12°

5) When the measure of one interior angle (regular polygon), 180×(n - 2)/n = 150°, we have;

180°·n - 2×180° - 150°·n = 0

30°·n = 360°

n = 360°/30° = 12

n = 12

The exterior angle sum = 360°

The measure of one exterior angle (regular polygon) = 360°/12 = 30°

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