Decagon

Elementary School

Definition

A ten sided polygon. A regular decagon will have sides that are all congruent with the same interior angles. The sum of its angles measures 1,440 degrees when seen from above, meaning each angle equals 144 degrees. Its central angle totals to 360 degrees.

Worked examples

\(\)Sum of interior angles\( = (10 - 2) \times 180^\circ = 8 \times 180^\circ = 1440^\circ\)

A decagon has 10 sides, so use \(n = 10\) in the polygon angle-sum formula \((n-2) \times 180^\circ\).

\(\)Each interior angle of a regular decagon\( = \frac{1440^\circ}{10} = 144^\circ\)

Divide the total interior angle sum by 10 to find each angle in a regular decagon.

Common mistakes

\(\)Sum\( = 10 \times 180^\circ = 1800^\circ\) → \(\)Sum\( = (10 - 2) \times 180^\circ = 1440^\circ\) Use \(n - 2\) triangles, not \(n\) triangles, when finding the interior angle sum of an \(n\)-gon.
Each exterior angle of a regular decagon is \(144^\circ\) → Each exterior angle is \(36^\circ\) (or \(\frac{360^\circ}{10}\)) Exterior angles sum to \(360^\circ\); interior and exterior angles are supplementary, so \(180^\circ - 144^\circ = 36^\circ\).
All decagons have \(144^\circ\) angles → Only regular decagons have all angles equal to \(144^\circ\) Irregular decagons have varying angles that still sum to \(1440^\circ\) but are not all congruent.

Where you'll use it next

You'll use decagons when working with general polygon formulas, studying tessellations, and solving problems about perimeter and area of regular polygons in geometry and trigonometry.

Found in 1 StudyPug lesson

Mastering Polygon Classification in Geometry

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Dive into the world of polygons! Learn to identify and classify shapes, understand their properties, and discover real-world applications. Enhance your geometry skills with our comprehensive guide.

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