Interior Angles: What They Are and Why They Matter

In geometry, you will encounter angles of all shapes and sizes. One type of angle that you will learn about is called an interior angle. Interior angles are formed when two lines intersect each other. The point where the lines intersect is called the vertex of the angle. The two lines that form the angle are called the sides of the angle.

The measure of an interior angle is determined by the number of degrees between the two sides of the angle. A degree is a unit of measurement for angles. One degree is equal to 1/360th of a full rotation. The symbol for degrees is °.

To measure an interior angle, you can use a protractor. A protractor is a tool that is used to measure angles. Protractors have a semicircular scale that is marked with degrees. To use a protractor, place the center of the protractor on the vertex of the angle. Then, align one side of the protractor with one side of the angle. Finally, read the number of degrees on the protractor that corresponds to the other side of the angle.

Interior angles are important in geometry because they are used to determine the properties of shapes. For example, the sum of the interior angles of a triangle is always 180 degrees. This means that if you know the measures of two interior angles of a triangle, you can find the measure of the third interior angle.

Interior angles are also used to classify polygons. A polygon is a closed figure that has at least three sides. Polygons are classified by the number of sides they have. For example, a triangle has three sides, a quadrilateral has four sides, and a pentagon has five sides.

The sum of the interior angles of a polygon is determined by the number of sides the polygon has. The formula for finding the sum of the interior angles of a polygon is:

Sum of interior angles = (n - 2) x 180°

where n is the number of sides of the polygon.

For example, the sum of the interior angles of a triangle is:

(3 - 2) x 180° = 180°

This means that the sum of the interior angles of a triangle is always 180 degrees.

Interior angles are a fundamental concept in geometry. They are used to determine the properties of shapes and to classify polygons. By understanding interior angles, you will be able to better understand geometry and the world around you.