A nonagon is a polygon that has nine sides. In the figure below are several types of nonagons.

You are watching: Find the sum of the interior angles of a nonagon

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Nonagon classifications

Like other polygons, a nonagon have the right to be classified as continual or irregular. If all the sides and also interior angles of a nonagon are equal, that is a continuous nonagon. Otherwise that is an rarely often, rarely nonagon.

Regular nonagonIrregular nonagon
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All sides and interior angles room equalNot every sides and also angles space equal

Nonagons and other polygons can additionally be classified together either convex or concave. If all inner angles of a nonagon are less than 180°, that is convex. If one or much more interior angle is larger than 180°, it is concave. A consistent nonagon is a convex nonagon.

Convex nonagonConcave nonagon
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All inner angles 180°

Diagonals that nonagon

A diagonal line is a line segment joining two non-consecutive vertices. A total of twenty-seven distinct diagonals deserve to be attracted for a nonagon. The following number is an example.

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There are 6 diagonals extending from each of the 9 vertices of the nonagon above creating a full of 27 diagonals.

Internal angle of a nonagon

The amount of the interior angles of a nonagon amounts to 1260°.

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As displayed in the number above, 6 diagonals deserve to be attracted to division the nonagon right into seven triangles. The blue lines over show just one way to divide the nonagon right into triangles; there are others. The amount of inner angles the the 7 triangles amounts to the sum of inner angles the the nonagon. Because the amount of the inner angles of a triangle is 180°, the sum of the internal angles the the nonagon is 9 × 180° = 1260°.

Regular nonagon

A continual nonagon is a nonagon in which every sides have actually equal length and all interior angles have equal measure.

Angles that a regular nonagon

Since every of the nine interior angles in a consistent nonagon room equal in measure, each inner angle actions 1260° ÷ 9 = 140°, as displayed below.

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Each exterior edge of a continual nonagon has actually an same measure the 40°.

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Symmetry in a constant nonagon

A continual nonagon has actually 9 currently of symmetry and also a rotational the opposite of stimulate 9, definition that it can be rotated in such a method that it will certainly look the same as the original shape 9 time in 360°.

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Lines that symmetryRotational symmetry
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9 present of symmetryNine 40° of rotation around the center.