A regular octagon is a polygon with eight equal sides and eight equal angles. To find the measure of an interior angle of a regular polygon, you can use the following formula:
Interior Angle = ((n – 2) * 180) / n
Where n is the number of sides in the polygon. For a regular octagon, n = 8.
Now, substituting the value of n into the formula:
Interior Angle = ((8 – 2) * 180) / 8
Interior Angle = (6 * 180) / 8
Interior Angle = 1080 / 8
Interior Angle = 135
Thus, each interior angle of a regular octagon measures 135 degrees.
Understanding the measurement of interior angles is important not only in geometry but also in various applications such as architecture, design, and art, where the octagonal shapes often appear. Whether you’re constructing an octagonal gazebo or designing an octagon-themed logo, knowing these angles helps achieve symmetry and balance.