## interior angle

### In geometry, an interior angle is an angle formed between two sides of a polygon on the inside of the shape

In geometry, an interior angle is an angle formed between two sides of a polygon on the inside of the shape. Specifically, it is an angle that is formed by two adjacent sides of the polygon, with its vertex at one of the polygon’s interior points.

To understand interior angles better, let’s consider a triangle as an example. In a triangle, each of the three interior angles is formed by two sides of the triangle and lies inside the shape. The sum of the interior angles of a triangle is always 180 degrees, which means that if you add up all three angles, the result will be 180 degrees.

For polygons with more sides, such as a quadrilateral or pentagon, the sum of the interior angles follows a similar pattern. The formula to find the sum of the interior angles of a polygon with n sides is (n – 2) * 180 degrees.

Each interior angle in a polygon can also be calculated by dividing the sum of the interior angles by the number of sides. For example, in a quadrilateral (a polygon with four sides), the sum of the interior angles is (4 – 2) * 180 = 360 degrees. Divide 360 degrees by 4, and each interior angle of the quadrilateral measures 90 degrees.

Understanding interior angles is crucial in various areas of mathematics, such as geometry and trigonometry. They help determine the properties and relationships between different polygons and assist in solving problems and making calculations involving angles within shapes.

##### More Answers:

Understanding the Isosceles Triangle Theorem | Exploring Congruent Angles in Isosceles TrianglesThe Importance and Characteristics of Remote Interior Angles in Geometry

Understanding the Exterior Angle Theorem | Relationship Between Exterior and Interior Angles in a Triangle