Question

If the sum of interior angles in a closed traverse is 1080º, then the number of sides in a traverse is

• A. 10
• B. 8
• C. 7
• D. 6

Hint:

Memorize the formula for the sum of interior angles of a polygon: $(n-2) \times 180^\circ$.
You can quickly check it with simple shapes:
- Triangle ($n=3$): $(3-2) \times 180 = 180^\circ$.
- Rectangle ($n=4$): $(4-2) \times 180 = 360^\circ$.

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The question asks for the number of sides ($n$) of a closed polygon (traverse) given the theoretical sum of its interior angles.

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

Step 3: Detailed Explanation:
We are given that the sum of the interior angles is $1080^\circ$. We can set this equal to the formula and solve for $n$. Using the second formula is easier.
\[ (n - 2) \times 180^\circ = 1080^\circ \] Divide both sides by $180^\circ$:
\[ n - 2 = \frac{1080}{180} \] \[ n - 2 = \frac{108}{18} = 6 \] \[ n = 6 + 2 \] \[ n = 8 \] The traverse has 8 sides.

Step 4: Final Answer:
The number of sides in the traverse is 8.