Interior Angles of a Polygon

This page focuses on the interior angles of polygons and provides a formula for calculating their sum. It presents visual examples of polygons with different numbers of sides and their corresponding interior angle sums.

The page introduces the formula for calculating the sum of interior angles of a polygon:

Formula: Sum of interior angles of polygons formula: $n-2$ × 180°, where 'n' is the number of sides.

The page provides examples of this formula applied to polygons with varying numbers of sides, from triangles (3 sides) to 17-sided polygons.

Example: For a pentagon (5 sides), the sum of interior angles is calculated as: $5-2$ × 180° = 540°

Highlight: The formula works for both regular and irregular polygons, as long as you know the number of sides.

Polygon Angle Calculations

This page presents practical examples of calculating angles in polygons using the interior angle sum formula. It demonstrates how to solve for unknown angles in both regular and irregular polygons.

Example 1: Finding an unknown angle in a 6-sided polygon The page walks through the process of calculating an unknown angle 'x' in a hexagon, given the measures of the other angles.

Example: In a 6-sided polygon with known angles of 110°, 130°, 60°, 70°, and 170°, the unknown angle 'x' is calculated to be 260°.

Example 2: Determining an angle in a regular polygon This example shows how to find the measure of each angle in a regular 12-sided polygon.

Example: In a regular 12-sided polygon, each interior angle measures 150°.

Example 3: Identifying a polygon from its interior angle sum The final example demonstrates how to determine the number of sides in a regular polygon given the sum of its interior angles.

Example: A regular polygon with a sum of interior angles of 1440° is identified as a decagon (10-sided polygon).

Highlight: These examples showcase the versatility of the interior angle sum formula in solving various polygon-related problems.

Interior and Exterior Angles of a Polygon

This page introduces the concept of polygons and their types. It explains the origin of the word "polygon" from Greek and defines it as a two-dimensional shape with multiple sides made of straight lines that form a closed shape.

The page distinguishes between two types of polygons:

1. Regular Polygons: These have all sides of equal length and all angles of the same size.

2. Irregular Polygons: These have sides of different lengths and angles of different sizes.

Vocabulary: A polygon is a two-dimensional shape with multiple sides made of straight lines that form a closed shape.

Example: Regular polygons include equilateral triangles, squares, regular pentagons, hexagons, heptagons, and octagons.

Highlight: The key difference between regular and irregular polygons lies in the consistency of their side lengths and angle sizes.