Decagon

A decagon is a polygon with 10 sides and 10 angles. The sum of the interior angles in a decagon is 1440 degrees. Each interior angle in a regular decagon measures 144 degrees.

Properties of a Decagon:

1. Number of Sides: A decagon has 10 sides.
2. Number of Angles: A decagon has 10 angles.
3. Interior Angles: The sum of the interior angles in a decagon is 1440 degrees.
4. Measure of Each Interior Angle: In a regular decagon, each interior angle measures 144 degrees.
5. Sum of Exterior Angles: The sum of the exterior angles in a decagon is always 360 degrees.

Formulas and Calculations:

To find the sum of the interior angles in a decagon, you can use the formula:

Sum of Interior Angles = (n - 2) * 180

Where n is the number of sides, so for a decagon, n = 10. Therefore:

Sum of Interior Angles = (10 - 2) * 180 = 8 * 180 = 1440 degrees

For a regular decagon, where all the sides and angles are equal, you can find the measure of each interior angle using the formula:

Measure of Each Interior Angle = Sum of Interior Angles / Number of Sides

For a decagon, the measure of each interior angle is:

Measure of Each Interior Angle = 1440 / 10 = 144 degrees

Example Problem:

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

Solution: Using the formula, we can calculate:

Measure of Each Interior Angle = Sum of Interior Angles / Number of Sides

Measure of Each Interior Angle = 1440 / 10 = 144 degrees

Practice Problems:

1. Find the sum of the interior angles in a decagon.
2. Find the measure of each interior angle in a regular decagon.
3. Calculate the sum of the exterior angles in a decagon.

Hope this study guide helps you understand the topic of decagons better!