Question

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what is the measure of each interior angle of a regular octagon?
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Explanation:

Step1: Recall the formula for the sum of interior angles

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), divide the sum of interior angles by the number of sides \(n\).
\(\frac{1080^{\circ}}{8}=135^{\circ}\)

Answer:

\(135\)