Discussion
The sum of the interior angles of a closed traverse having N number of sides is equal to :
Answer: B
The sum is (N−2)×180°.
Any closed polygon with N sides can be divided into N − 2 triangles from one vertex, each with angles adding to 180°. So the interior angles of a closed traverse must total (N − 2) × 180°, which is the angular check applied in the field.
For a quadrilateral, N = 4 gives 360°, as it should. (N − 4) × 180° would give zero for the same figure, and (N − 1) or (2N − 1) give 540° and 1260°, too large. The same rule is often written in right angles as (2N − 4) × 90°.
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