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Regular Polygons

With equal angles and equal side lengths, what more could you want from a polygon?

Level 1

         

Regular \(n\)-gonInternal Angle Sum
3180
4360
5540
6720

Given the pattern seen in this table, which of the following accurately represents the internal angle sum in terms of \( n \)?

If \(FGHIJ\) is a regular pentagon, find \[\angle A + \angle B + \angle C + \angle D + \angle E \ .\]

Details: A regular pentagon is a pentagon with 5 sides of equal length and 5 corner angles of equal measure.

What is the area of the red region if the blue region is 5?

Note: The hexagon is regular.

Which of the following is the ratio between the interior angle of a 24 sided regular polygon to the interior angle of a 12 sided regular polygon?

Consider that in the above image the triangle is right angled and the octagon is regular. Then find \(x\) in degrees.

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