Question

If the sum of the interior angles of a polygon is \(1260^\circ\), how many sides does it have?

• A. 7
• B. 9
• C. 10
• D. 8

Hint:

To find the number of sides of a polygon from the sum of interior angles, use the formula: \((n - 2) \times 180^\circ = \text{sum of interior angles}\). Solve for \(n\).

Answer 1

The Correct Option is B

Step 1: Use the formula for the sum of interior angles of a polygon.
The sum of the interior angles of an \(n\)-sided polygon is given by: \[ \text{Sum of interior angles} = (n - 2) \times 180^\circ \] Step 2: Plug in the given sum.
We are given that the sum is \(1260^\circ\). So, we set up the equation: \[ (n - 2) \times 180 = 1260 \] Step 3: Solve for \(n\). \[ n - 2 = \frac{1260}{180} = 7 \Rightarrow n = 7 + 2 = 9 \] Hence, the polygon has \({9}\) sides.