The sum of interior angles of a closed traverse is -a)(n-2)x180ob)(n-...
For closed traverses, Sum of Interior angles = (n-2) x 180°, where n = number of angles in the traverse.
Hence the correct answer is option A.
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The sum of interior angles of a closed traverse is -a)(n-2)x180ob)(n-...
The sum of interior angles of a closed traverse is given by the formula (n-2) x 180o, where n is the number of sides or vertices in the traverse. In this case, the correct answer is option 'A' which states that the sum of interior angles is -a)(n-2) x 180o. Let's understand why this is the correct answer.
Explanation:
- The sum of interior angles in any polygon can be found by dividing the polygon into triangles. Since a triangle has interior angles that add up to 180o, the sum of interior angles in a polygon with n sides can be found by dividing it into (n-2) triangles.
- To visualize this, imagine drawing a diagonal from one vertex of the polygon to all the other vertices. This will divide the polygon into (n-2) triangles.
- Each triangle will have interior angles that add up to 180o. Therefore, the sum of interior angles in the entire polygon will be (n-2) x 180o.
Let's consider an example:
- Suppose we have a polygon with 6 sides or vertices (hexagon).
- If we divide this hexagon into triangles by drawing diagonals, we will get 4 triangles.
- Each triangle has interior angles that add up to 180o, so the sum of interior angles in these 4 triangles will be 4 x 180o = 720o.
- Applying the formula (n-2) x 180o, we get (6-2) x 180o = 4 x 180o = 720o, which matches our result.
Conclusion:
- The correct answer is option 'A' which states that the sum of interior angles of a closed traverse is -a)(n-2) x 180o.
- This formula is derived from dividing the polygon into triangles and noting that each triangle has interior angles that add up to 180o.
- By applying this formula, we can easily calculate the sum of interior angles for any closed traverse.