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.

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

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)

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.

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.

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.

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:

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!

.Study GuideGeometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key

Geometric Proportions Worksheet/Answer key Numerical & Geometric Proportions

Number and Operations (NCTM)

Compute fluently and make reasonable estimates.

Develop, analyze, and explain methods for solving problems involving proportions, such as scaling and finding equivalent ratios.

Geometry (NCTM)

Analyze characteristics and properties of two- and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships.

Understand relationships among the angles, side lengths, perimeters, areas, and volumes of similar objects.

Create and critique inductive and deductive arguments concerning geometric ideas and relationships, such as congruence, similarity, and the Pythagorean relationship.

Measurement (NCTM)

Apply appropriate techniques, tools, and formulas to determine measurements.

Solve problems involving scale factors, using ratio and proportion.

Connections to the Grade 7 Focal Points (NCTM)

Measurement and Geometry: Students connect their work on proportionality with their work on area and volume by investigating similar objects. They understand that if a scale factor describes how corresponding lengths in two similar objects are related, then the square of the scale factor describes how corresponding areas are related, and the cube of the scale factor describes how corresponding volumes are related. Students apply their work on proportionality to measurement in different contexts, including converting among different units of measurement to solve problems involving rates such as motion at a constant speed. They also apply proportionality when they work with the circumference, radius, and diameter of a circle; when they find the area of a sector of a circle; and when they make scale drawings.