Geometry

Question Analysis

The main focus of this question is to calculate the measure of one interior angle of a regular octagon. It tests the understanding of the formula used to find the interior angles of regular polygons.

 

Key Concept Explanation

Measure of an interior angle () of a regular polygon: The formula for calculating the measure of an interior angle of a regular polygon with sides is . This formula is derived from the fact that the sum of the interior angles of a polygon is , and in a regular polygon, all interior angles are equal.

 

Step - by - Step Solution

1. Identify the number of sides:

For an octagon, .

2. Substitute into the formula:

First, calculate :

Substitute into , we get .

Then, find :

.

Finally, divide by to find the measure of one interior angle:

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