Question
Download Solution PDFFor n number of sides, the total sum of interior angles of a closed traverse is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Sum of Interior Angles of a Closed Traverse
The sum of the interior angles of a closed traverse with n sides is derived using the formula for the sum of interior angles of a polygon. The general formula for the sum of interior angles of a polygon with n sides is:
Sum of interior angles = (n - 2) × 180°
This formula is derived from the fact that a polygon with n sides can be divided into (n - 2) triangles, and each triangle has an angle sum of 180°.
Now, since the question specifies the sum of angles in terms of multiples of 90°, we rewrite the formula:
Sum of interior angles = (n - 2) × 180° = (2n - 4) × 90°
Thus, the total sum of the interior angles of a closed traverse with n sides is:
(2n - 4) × 90°
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