Question

5
determine the number of sides for a polygon given the sum of its interior angles.
given: sum of interior angles = 1080°
number of sides =

type of polygon:

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 are given that \( S = 1080^{\circ} \). Substitute this into the formula:

$$ 1080=(n - 2)\times180 $$

First, divide both sides of the equation by \( 180 \):

$$ \frac{1080}{180}=n - 2 $$

\( \frac{1080}{180}=6 \), so we have:

$$ 6=n - 2 $$

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

$$ n=6 + 2=8 $$

A polygon with 8 sides is called an octagon.

Answer:

number of sides = \( 8 \)
type of polygon: octagon