Question

i) Can 127° be the interior angle of a regular polygon?

ii) In a pentagon, the measures of the 4 angles 2x°, 3x°, 4x°, 5x° and the fifth angle is 120°. Find all the angles.​

Answer 1

Step-by-step explanation:

1. A regular polygon with 127 sides where the length of each side is 4 units. The units may either be inches or cm or km or miles: any unit of length.

You are given a Regular Polygon with 127 sides. What are the interior angles and exterior angles?

If the length of each side is 4 units, what is the perimeter, area, circum-radius and in-radius of the polygon?

n = 127

Perimeter of a polygon with 127 sides = (side length) x 127 = 508 units

Area of a polygon with 127 sides = (n x Side2 x cot (Π/n))/4 = (n x 42 x cot (Π/127))/4 = 20531.89 square units

Sum of the interior angles of a polygon with 127 sides = (n-2) x 180 degrees = (127-2) x 180 degrees = 22500 degrees

Interior Angle of a polygon with 127 sides = (n-2) x 180/n degrees = (127-2) x 180/127 degrees = 177.16 degrees

Exterior angle of a polygon with 127 sides = 180 - Interior Angle = 180 - 177.16 = 2.83 degrees

Inradius = Radius of In-circle = (side length) x cot (Π/127) = 4 x cot 1 = 161.66 units

Circumradius = Radius of Circum-circle = (side length) x cosec (Π/127) = 4 x cosec 1 degrees = 161.71 units

Symmetry Group = D127 127 rotational symmetries and 127 reflection symmetries. The "D" stands for di-hedral.

2)total sum of angles = 540

so equation will be 2x + 3x + 4x + 5x + 120 = 540

now , 14x + 120 = 540

14x = 420

x = 30

therefore

2x = 60

3x = 90

4x = 120

5x = 150

and last angle was given = 120

so 120 + 120 +150 +90 +60 = 540

Mark as brainlist