Properties of Polygons

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Polygons:

▪ If all sides and all angles are equal, then the polygon is a regular polygon
▪ A regular polygon of n sides has n(n-3)/2 diagonals
▪ In a regular polygon of n sides, each exterior angle is 360/n degrees.
▪ Sum of measure of all the interior angles of a regular polygon is 180 (n-2) degrees (where n is the number of sides of the polygon)
▪ Each interior angle = 180(n−2)/n
▪ The sum of the measures of all the exterior angles of a regular polygon is 360 degrees.

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    Question 1

    In a polygon, all the interior angles are either 90 degrees or 270 degrees. If the number of interior angles which are 90 degrees is 31, find the number of angles which are 270 degrees?

    Question 2

    A regular polygon of n sides is inscribed in a circle of radius 1. Another regular polygon of 'm' sides is circumscribed on the same circle. Let the perimeter of the inscribed polygon be denoted by $$P_i(n)$$, and that of the circumscribed polygon be denoted by $$P_c(m)$$. Which of the following is true about $$\frac{P_c(7)+2\pi}{P_i(14)}$$?

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