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°
