Decagon

A decagon is a ten-sided polygon. The sum of the interior angles of a decagon is always 1440 degrees, and each interior angle of a regular decagon measures 144 degrees.

Properties of a Decagon

• A decagon has 10 sides and 10 vertices.
• The sum of the interior angles of a decagon is given by the formula: Sum = (n-2) * 180°, where n is the number of sides. So for a decagon, the sum is: (10-2) * 180° = 8 * 180° = 1440°
• In a regular decagon, each interior angle measures: 144°
• The exterior angles of a decagon add up to 360 degrees.

How to Find the Measure of Each Interior Angle

To find the measure of each interior angle in a regular decagon, you can use the formula: Interior angle = Sum of interior angles / Number of sides. For a regular decagon, this would be: 1440° / 10 = 144°

Sample Problems

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

Solution: Using the formula, we have: Interior angle = 1440° / 10 = 144°

2. Find the sum of the interior angles in a decagon.

Solution: Using the formula Sum = (n-2) * 180°, we have: (10-2) * 180° = 1440°

Practice Questions

1. What is the sum of the interior angles of a decagon?
2. Find the measure of each interior angle in a regular decagon.
3. If the measure of one interior angle in a decagon is 150°, is the decagon regular or irregular?

Hope this study guide helps in understanding the topic of decagon!