how many sides does a polygon have if the sum of the interior angles is 360°?

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} $, where $ S $ is the sum of the interior angles and $ n $ is the number of sides.
## Step2: Substitute the given sum into the formula and solve for $ n $
We know that $ S = 360^{\circ} $. Substitute this into the formula:
$$
\begin{align*}
360^{\circ}&=(n - 2)\times180^{\circ}\
\frac{360^{\circ}}{180^{\circ}}&=n - 2\
2&=n - 2\
n&=2 + 2\
n&=4
\end{align*}
$$
# Answer:
The polygon has 4 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: