Decagon classifications

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

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Regular decagonIrregular dodecagon
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All sides and interior angles room 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 type of two point out on its boundary lies exterior of it. None of the inner angles is higher than 180°. Think the a convex decagon together bulging outwards, like the continuous decagon above.

Conversely, a concave decagon, choose the rarely often, rarely decagon presented above, contends least one-line segment that deserve to be drawn in between points on its boundary, but lies exterior of it. Also, at the very least one of its interior angles is higher than 180°

A convex decagon does not need to be a constant decagon. Yet, a regular decagon is always a convex decagon.

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The decagon over is convex but plainly has sides and also angles that space not congruent. This decagon is irregular. Also, no component of any kind of segment drawn between two boundary points, such as AB, lies external of the decagon.

Angles that a decagon

Decagons deserve to be broken into a series of triangle by diagonals attracted from that is vertices. This series of triangles can be provided to discover the sum of the internal angles of the decagon.

Diagonals are drawn from crest A in the convex decagon below, creating 8 triangles. Similarly, 8 triangle can additionally be attracted in a concave decagon. Since the amount of the angle of a triangle is 180°, the sum of the inner angles that a dodecagon is 8 × 180° = 1440°.

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A continuous decagon has actually equal interior angle measures. Since 1440°/10 = 144°, each interior angle in a continual decagon has actually a measure of 144°. Also, each exterior angle has actually a measure of 36°.

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A continuous decagon deserve to be inscriptions in a circle. Each vertex top top the decagon lies on the circle. Also, the circle and decagon re-superstructure the exact same center.