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

    Regular polygons A and B have number of sides in the ratio 1 : 2 and interior angles in the ratio 3 : 4. Then the number of sides of B equals

    Question 2

    In a regular polygon, any interior angle exceeds the exterior angle by 120 degrees. Then, the number of diagonals of this polygon is

    Question 3

    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?

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