A decagon is a polygon with 10 sides and 10 angles. The sum of the interior angles in a decagon is 1440 degrees. Each interior angle in a regular decagon measures 144 degrees.

**Number of Sides:**A decagon has 10 sides.**Number of Angles:**A decagon has 10 angles.**Interior Angles:**The sum of the interior angles in a decagon is 1440 degrees.**Measure of Each Interior Angle:**In a regular decagon, each interior angle measures 144 degrees.**Sum of Exterior Angles:**The sum of the exterior angles in a decagon is always 360 degrees.

To find the sum of the interior angles in a decagon, you can use the formula:

**Sum of Interior Angles = (n - 2) * 180**

Where *n* is the number of sides, so for a decagon, *n* = 10. Therefore:

**Sum of Interior Angles = (10 - 2) * 180 = 8 * 180 = 1440 degrees**

For a regular decagon, where all the sides and angles are equal, you can find the measure of each interior angle using the formula:

**Measure of Each Interior Angle = Sum of Interior Angles / Number of Sides**

For a decagon, the measure of each interior angle is:

**Measure of Each Interior Angle = 1440 / 10 = 144 degrees**

**Question:** Find the measure of each interior angle in a regular decagon.

**Solution:** Using the formula, we can calculate:

**Measure of Each Interior Angle = Sum of Interior Angles / Number of Sides**

**Measure of Each Interior Angle = 1440 / 10 = 144 degrees**

- Find the sum of the interior angles in a decagon.
- Find the measure of each interior angle in a regular decagon.
- Calculate the sum of the exterior angles in a decagon.

Hope this study guide helps you understand the topic of decagons better!

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Number and Operations (NCTM)

Understand numbers, ways of representing numbers, relationships among numbers, and number systems.

Understand and use ratios and proportions to represent quantitative relationships.

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.

Apply transformations and use symmetry to analyze mathematical situations.

Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.

Measurement (NCTM)

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

Solve problems involving scale factors, using ratio and proportion.

Grade 8 Curriculum Focal Points (NCTM)

Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle

Students use fundamental facts about distance and angles to describe and analyze figures and situations in two- and three-dimensional space and to solve problems, including those with multiple steps. They prove that particular configurations of lines give rise to similar triangles because of the congruent angles created when a transversal cuts parallel lines. Students apply this reasoning about similar triangles to solve a variety of problems, including those that ask them to find heights and distances. They use facts about the angles that are created when a transversal cuts parallel lines to explain why the sum of the measures of the angles in a triangle is 180 degrees, and they apply this fact about triangles to find unknown measures of angles. Students explain why the Pythagorean Theorem is valid by using a variety of methods - for example, by decomposing a square in two different ways. They apply the Pythagorean Theorem to find distances between points in the Cartesian coordinate plane to measure lengths and analyze polygons and polyhedra.