Question

If \( n \) is the number of sides of a traverse, the theoretical sum of the interior included angles of a closed traverse is:

• A. \( (2n - 4) \times 90^\circ \)
• B. \( (2n + 4) \times 90^\circ \)
• C. \( (2n \pm 4) \times 90^\circ \)
• D. \( 360^\circ \)

Hint:

Use \( (2n - 4) \times 90^\circ \) for sum of interior angles in closed traverses.

Answer 1

The Correct Option is A

If \( n \) is the number of sides of a traverse, it is essentially a polygon with \( n \) sides. The formula to find the sum of the interior angles of a polygon with \( n \) sides is given by:

\( (n-2) \times 180^\circ \)

This formula comes from dividing the polygon into \( (n-2) \) triangles, each having an angle sum of \( 180^\circ \). Now, since a closed traverse is also a polygon, we can apply this same formula to find the sum of its interior angles. Simplifying the expression, we want to express it in terms of \( 90^\circ \).

Notice that \( 180^\circ = 2 \times 90^\circ \). Therefore, we can rewrite the original angle sum formula as:

\( (n-2) \times 180^\circ = (n-2) \times 2 \times 90^\circ = (2n-4) \times 90^\circ \)

Thus, the theoretical sum of the interior angles of a closed traverse is:

\( (2n-4) \times 90^\circ \)

This confirms that the correct answer is Option 1: \( (2n-4) \times 90^\circ \).