Decagon

A decagon is a polygon with 10 sides and 10 angles. The sum of the interior angles of a decagon is always 1440 degrees. Each interior angle of a regular decagon measures 144 degrees. The formula to find the sum of the interior angles of a decagon is: S = (n-2) * 180, where S is the sum of the interior angles and n is the number of sides.

Properties of a Decagon:

• A decagon has 10 sides, 10 vertices, and 10 angles.
• The sum of the interior angles of a decagon is 1440 degrees.
• Each interior angle of a regular decagon measures 144 degrees.
• The sum of the exterior angles of a decagon is always 360 degrees.

Formulas for Decagon:

• Sum of interior angles: S = (n-2) * 180
• Measure of each interior angle in a regular decagon: A = 144 degrees
• Sum of exterior angles: 360 degrees

Examples:

Example 1: Find the sum of the interior angles of a decagon.

Solution: S = (10-2) * 180 = 8 * 180 = 1440 degrees

Example 2: Find the measure of each interior angle in a regular decagon.

Solution: A = 144 degrees

Example 3: Find the sum of the exterior angles of a decagon.

Solution: 360 degrees

Practice Problems:

1. Find the measure of each interior angle in a regular decagon.

2. Calculate the sum of the interior angles of a decagon with 12 sides.

3. Determine the sum of the exterior angles of a decagon.

After solving these practice problems, you should have a good understanding of the properties and formulas related to decagons. Good luck!