Octagon

An octagon is a polygon with eight sides and eight angles. The sum of the interior angles of an octagon is 1080 degrees.

Properties of an Octagon:

• Number of Sides: 8
• Number of Angles: 8
• Sum of Interior Angles: 1080 degrees
• Sum of Exterior Angles: 360 degrees
• Lines of Symmetry: 8

Formulas for Octagon:

Sum of interior angles = (n-2) * 180 where n is the number of sides

Sum of exterior angles = 360 degrees

Number of diagonals = n(n-3)/2 where n is the number of sides

How to Calculate the Interior and Exterior Angles of an Octagon:

To find the measure of each interior angle of a regular octagon, use the formula: Interior angle = (Sum of interior angles) / Number of sides. For an octagon, this would be: Interior angle = 1080 / 8 = 135 degrees.

To find the measure of each exterior angle of a regular octagon, use the formula: Exterior angle = 360 / Number of sides. For an octagon, this would be: Exterior angle = 360 / 8 = 45 degrees.

Examples of Octagon:

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Real-life Examples of Octagon:

Stop signs, nuts, and bolts, and certain building designs often feature octagonal shapes.

Conclusion:

Understanding the properties and formulas related to octagons is essential for solving problems related to geometry and spatial reasoning.