Question 74

Each side of a given polygon is parallel to either the X or the Y axis. A corner of such a polygon is said to be convex if the internal angle is 90° or concave if the internal angle is 270°. If the number of convex corners in such a polygon is 25, the number of concave corners must be

Solution

Let the total number of sides be x.

Sum of internal angles in a polygon = (x-2)*180 where x is the number of sides.

It is given that the polygon has 25 convex sides, then the number of concave sides = x-25

(25*90)+(x-25)*270 = (x-2)180

x = 46

Number concave corners = x-25 = 46-25 = 21

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