Hexagon

A hexagon is a polygon with six sides and six angles. The sum of the interior angles in a hexagon is always 720 degrees. Each interior angle of a regular hexagon measures 120 degrees.

Types of Hexagons

There are two main types of hexagons: regular and irregular.

Regular Hexagon

A regular hexagon has all its sides and angles equal in measure. The formula to find the interior angle of a regular hexagon is:

Interior Angle = 180 - ((6-2) * 180 / 6)

Irregular Hexagon

An irregular hexagon has sides and/or angles of different measures. The sum of the interior angles in an irregular hexagon is still 720 degrees, but the measures of the angles and sides can vary.

Properties of Hexagons

Some important properties of hexagons include:

• A hexagon has six sides and six angles.
• The sum of the interior angles of a hexagon is always 720 degrees.
• A regular hexagon has equal sides and angles.
• The exterior angles of a hexagon add up to 360 degrees.

Example Problems

1. Find the measure of each interior angle of a regular hexagon.

Interior Angle = 180 - ((6-2) * 180 / 6) = 120 degrees

2. If the measure of one interior angle of an irregular hexagon is 130 degrees, what is the measure of the remaining interior angles?

Sum of interior angles = 720 degrees

Sum of the remaining angles = 720 - 130 = 590 degrees

Since an irregular hexagon can have different measures for each angle, the remaining angles can vary.

Practice Problems

1. Find the measure of each interior angle of a regular hexagon with a side length of 5 cm.

2. Determine whether the following shapes are hexagons:

• a. A shape with six sides of different lengths.
• b. A shape with six sides, each measuring 8 cm.

3. If the sum of the interior angles of a hexagon is 900 degrees, is the hexagon regular or irregular? Explain your reasoning.

Remember, practice is key to mastering the concepts of hexagons. Good luck!