Polygons

Find diagonal and angle relationships to calculate polygon angles.

Meaning

A polygon is a closed plane figure made of joined segments. Triangulating a simple -gon gives interior-angle sum degrees.

Example

Two diagonals from a vertex divide a convex pentagon into three triangles. Its angle sum is degrees.Dividing the angle sum by the vertex count gives each angle only when all angles are equal. A general pentagon need not have five 108-degree angles.

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Scope and references

Topics

Polygons and regular polygons, diagonals, interior-angle sums, exterior angles

Learning goal

Find diagonal and angle relationships to calculate polygon angles.

Helpful background

Explore triangle angles and dividing shapes.

Polygons

These choice exercises use stated geometric conditions. They do not establish construction, drawing, spatial manipulation, written proof, or mastery of the whole geometry area.

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Polygons

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Polygons