Introduction:

The interior angle of a regular polygon is an important geometric concept. Regular polygons have equal sides and angles, and understanding these angles is crucial in various fields, including mathematics, architecture, and design.



Simple Explanation:



What is the Interior Angle of a Regular Polygon?



It's the angle formed between two adjacent sides inside the polygon.

In a regular polygon, all interior angles are equal.

Calculating the Interior Angle:



The sum of interior angles of a polygon with n sides is (n - 2) x 180 degrees.

To find the measure of each interior angle, divide this sum by n.

The formula is: (n - 2) x 180 / n.

Example:



Finding an Interior Angle:



For a regular pentagon (5 sides), calculate the interior angle like this:

(5 - 2) x 180 / 5 = 3 x 180 / 5 = 540 / 5 = 108 degrees.

So, each interior angle in a regular pentagon is 108 degrees.

Checking the Calculation:



Make sure you use the correct number of sides (n) in the formula.

Carefully do the multiplication and division.

Key Points to Remember:



The sum of interior angles goes up by 180 degrees for each additional side.

Knowing interior angles helps understand the properties of polygons.

Activity:



Try calculating interior angles for various regular polygons.

Draw these polygons and measure the angles to check your work.

Extra Tip:



Understanding these angles is helpful for more complex geometric concepts and practical applications.