Question

how many sides does a polygon have if the sum of the interior angles is 1260°?

Explanation:

Step1: Recall the formula for the sum of interior angles of a polygon

The formula for the sum of the interior angles of a polygon with \( n \) sides is \( S=(n - 2)\times180^{\circ} \), where \( S \) is the sum of the interior angles.

Step2: Substitute the given sum into the formula and solve for \( n \)

We are given that \( S = 1260^{\circ} \). Substituting this into the formula \( (n - 2)\times180^{\circ}=1260^{\circ} \). First, divide both sides of the equation by \( 180^{\circ} \):
\[

$$\begin{align*} n - 2&=\frac{1260^{\circ}}{180^{\circ}}\\ n - 2& = 7 \end{align*}$$

\]
Then, add 2 to both sides of the equation to solve for \( n \):
\[

$$\begin{align*} n&=7 + 2\\ n&=9 \end{align*}$$

\]

Answer:

The polygon has 9 sides.