Question

emily wants to construct a flower bed in the shape of a regular octagon (8 - sided convex polygon).
find the measure of each of the interior angles using the polygon interior angle sum theorem.
1080°
90°
720°

Explanation:

Step1: Recall the formula for the sum of interior angles

The formula for the sum of interior angles of a polygon is \(S=(n - 2)\times180^{\circ}\), where \(n\) is the number of sides. For an octagon, \(n = 8\).

$$S=(8 - 2)\times180^{\circ}=6\times180^{\circ}=1080^{\circ}$$

Step2: Find the measure of each interior angle

Since it is a regular octagon, all interior angles are equal. Let \(x\) be the measure of each interior angle. Then \(x=\frac{S}{n}\).

$$x=\frac{1080^{\circ}}{8}=135^{\circ}$$

But wait, there is a mistake in the options provided. If we assume there was a mis - input in the problem (maybe the user intended to ask for the sum of interior angles instead of each interior angle), and if we consider the sum of interior angles formula \(S=(n - 2)\times180^{\circ}\) with \(n = 8\)

$$S=(8 - 2)\times180^{\circ}=1080^{\circ}$$

Answer:

\(1080^{\circ}\) (assuming the question was misphrased and was asking for the sum of interior angles. If it was truly asking for each interior angle, there is an error in the given options as each interior angle of a regular octagon is \(135^{\circ}\))