Question

a regular polygon has 72 sides find the size of interior angle ​

Answer 1

Answer:

(b) Calculate the number of sides in the regular polygon. We do this by dividing 360° by the size of one exterior angle, which is 72°. The answer is 360° ÷ 72° = 5 sides.

Step-by-step explanation:

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Answer 2

Answer:

You are given a Regular Polygon with 72 sides. What are the interior angles and exterior angles?

If the length of each side is 10 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 72

Perimeter of a polygon with 72 sides = (side length) x 72 = 720 units

Area of a polygon with 72 sides = (n x Side2 x cot (Π/n))/4 = (n x 102 x cot (Π/72))/4 = 41226.77 square units

Sum of the interior angles of a polygon with 72 sides = (n-2) x 180 degrees = (72-2) x 180 degrees = 12600 degrees

Interior Angle of a polygon with 72 sides = (n-2) x 180/n degrees = (72-2) x 180/72 degrees = 175 degrees

Exterior angle of a polygon with 72 sides = 180 - Interior Angle = 180 - 175 = 5 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/72) = 10 x cot 2 = 229.03 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/72) = 10 x cosec 2 degrees = 229.25 units

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