Decagon classifications

Like various other polygons, a decagon have the right to be share as constant or irregular.

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Regular decagonIrregular dodecagon
All sides and also interior angles space congruentSides and angles have various lengths

A decagon can additionally be classified as convex or concave.

A convex decagon is a polygon whereby no heat segment between any two clues on its boundary lies outside of it. None of the internal angles is greater than 180°. Think of a convex decagon together bulging outwards, prefer the regular decagon above.

Conversely, a concave decagon, favor the irregular decagon displayed above, has at least one-line segment that deserve to be drawn in between points ~ above its boundary, yet lies external of it. Also, at the very least one of its internal angles is greater than 180°

A convex decagon go not have to be a regular decagon. Yet, a regular decagon is constantly a convex decagon.


The decagon above is convex but clearly has sides and angles that space not congruent. This decagon is irregular. Also, no component of any kind of segment drawn between two boundary points, such together AB, lies exterior of the decagon.

Angles of a decagon

Decagons can be damaged into a collection of triangles by diagonals drawn from that vertices. This series of triangles deserve to be supplied to uncover the amount of the interior angles of the decagon.

Diagonals are drawn from peak A in the convex decagon below, forming 8 triangles. Similarly, 8 triangles can additionally be drawn in a concave decagon. Because the amount of the angles of a triangle is 180°, the sum of the interior angles that a dodecagon is 8 × 180° = 1440°.


A consistent decagon has actually equal internal angle measures. Because 1440°/10 = 144°, each interior angle in a regular decagon has a measure up of 144°. Also, every exterior angle has actually a measure of 36°.

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A continual decagon can be inscribed in a circle. Every vertex ~ above the decagon lies top top the circle. Also, the circle and also decagon re-superstructure the same center.