Question

If the number of sides resulting in a closed traverse is increased from three to four, the sum of the interior angles increases by

• A. \( 90^\circ \)
• B. \( 180^\circ \)
• C. \( 270^\circ \)
• D. \( 360^\circ \)

Hint:

The sum of the interior angles of a polygon increases by \( 180^\circ \) with each additional side.

Answer 1

The Correct Option is B

Step 1: The formula for calculating the sum of interior angles of a polygon is: \[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \] Step 2: Calculating for a triangle (\( n = 3 \)): \[ (3 - 2) \times 180^\circ = 180^\circ \] Step 3: Calculating for a quadrilateral (\( n = 4 \)): \[ (4 - 2) \times 180^\circ = 360^\circ \] Step 4: Increase in the sum of interior angles when the number of sides increases from 3 to 4: \[ 360^\circ - 180^\circ = 180^\circ \] Conclusion: The sum of interior angles increases by \( 180^\circ \), hence the correct answer is option (B).