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

Question

Accepted Answer

# 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} $.
## Step2: Substitute the given sum into the formula and solve for $ n $
We are given that $ S = 1260^{\circ} $. Substituting this into the formula:
$$
\begin{align*}
1260^{\circ}&=(n - 2)\times180^{\circ}\
\frac{1260^{\circ}}{180^{\circ}}&=n - 2\
7&=n - 2\
n&=7 + 2\
n&=9
\end{align*}
$$
# Answer:
The polygon has 9 sides.

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QUESTION IMAGE

Question

Explanation:

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

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

Answer: