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densk [106]
3 years ago
8

What is the sum of the interior angles, each interior angle, the central angle, and each exterior angle of a pentagon, a hexagon

, an octogon, a nonagon, a decagon and a dodecagon.
Mathematics
1 answer:
WITCHER [35]3 years ago
3 0
<span>Sum of Interior Angles: Formula: (n-2) * 180
-Pentagon: 540</span>°<span>
-Hexagon: 720</span>°<span>
-Octagon: 900</span>°<span>
-Nonagon: 1260</span>°<span>
-Decagon: 1440</span>°<span>
-Dodecagon: 1800</span>°

Each interior Angle: Formula: [(n-2)*180] / n
-Pentagon: 108°
-Hexagon: 120°
-Octagon: 135°
-Nonagon: 140°
-Decagon: 144°
-Dodecagon: 150°

The sum of the exterior angles of each polygon stated above is equal to 360 degrees. Using the formula: (180-interior angle) * n

The central angle is formed by making a circle in the middle and divide it by the number of sides. Therefore, CA = 360 /n
-Pentagon: 72°
-Hexagon: 60°
-Octagon: 45°
-Nonagon: 40°
-Decagon: 36°
-Dodecagon: 30°

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