Decagon classifications

Like other polygons, a decagon deserve to be classified as continuous or irregular.

You are watching: Interior angle of a regular decagon

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

A decagon can likewise be classified as convex or concave.

A convex decagon is a polygon where no heat segment between any two points on its boundary lies outside of it. No one of the interior angles is greater than 180°. Think that a convex decagon together bulging outwards, like the consistent decagon above.

Conversely, a concave decagon, prefer the irregular decagon shown above, has at least one-line segment that can be drawn between points ~ above its boundary, yet lies exterior of it. Also, at least one of its internal angles is greater than 180°

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

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

Angles that a decagon

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

Diagonals are drawn from crest A in the convex decagon below, developing 8 triangles. Similarly, 8 triangle can also be drawn in a concave decagon. Since the sum of the angle of a triangle is 180°, the sum of the interior angles of a dodecagon is 8 × 180° = 1440°.

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A regular decagon has equal inner angle measures. Due to the fact that 1440°/10 = 144°, each interior angle in a consistent decagon has actually a measure up of 144°. Also, each exterior angle has actually a measure up of 36°.

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Did girlfriend know?

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