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For a Rectilinear (concave polygon having all sides parallel to either X or Y axis), how do we find the "sum of all the interior angles" given total number of convex corners (corner whose internal angle is 90 degrees).

For example - what will be the sum of all the interior angles of a rectilinear with 10 convex corners.

Any help is much appreciated.

Chintan S.
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1 Answers1

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The number of convex corners determines the number of concave corners. We can consider it as a rectangle with smaller rectangles cut out of some corner.

  • Starting with a rectangle, we have 4 convex corners and 0 concave corners.
  • Each move of removing a smaller rectangle increases the number of convex and concave corners by 1 each.

Consequently, the number of concave corners is $(\#$ convex corners$) - 4$. Now use what you know about the number of degrees in convex and concave corners.

Zvi Rosen
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