Question

A closed traverse of sides ABCDEF. The sum of interior angles of the traverse is

• A. 630\(^{\circ}\)
• B. 540\(^{\circ}\)
• C. 720\(^{\circ}\)
• D. 450\(^{\circ}\)

Hint:

It's helpful to remember the sum of interior angles for common polygons:
- Triangle (n=3): 180\(^{\circ}\) - Quadrilateral (n=4): 360\(^{\circ}\) - Pentagon (n=5): 540\(^{\circ}\) - Hexagon (n=6): 720\(^{\circ}\)

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
We need to calculate the theoretical sum of the interior angles of a closed traverse with a given number of sides.

Step 2: Key Formula or Approach:
The formula for the sum of the interior angles of a closed polygon (traverse) with 'n' sides is:
\[ \text{Sum of interior angles} = (n - 2) \times 180^{\circ} \] Alternatively, using right angles:
\[ \text{Sum of interior angles} = (2n - 4) \times 90^{\circ} \]

Step 3: Detailed Explanation:
The traverse is given as ABCDEF.
By counting the letters, we can determine the number of sides or vertices.
The vertices are A, B, C, D, E, F.
So, the number of sides, n = 6.
Now, we substitute n=6 into the formula:
\[ \text{Sum} = (6 - 2) \times 180^{\circ} \] \[ \text{Sum} = 4 \times 180^{\circ} \] \[ \text{Sum} = 720^{\circ} \]

Step 4: Final Answer:
The sum of the interior angles of the traverse is 720\(^{\circ}\).
This corresponds to option (C).