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Q: What is the total sum of its interior angles of a polygon that has 189 diagonals showing work?

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If all of the interior angles of the polygon add up to 180 degrees, then the polygon is a triangle.

The interior angles add up to 3600 degrees

A regular polygon is a polygon with congruent sides and interior angles.

The exterior and interior angles of each vertex of a polygon add up to 180 degrees.

Your polygon has 60 sides. Total interior angles 116 x 90 = 10440 degrees. This works because interior angles of any n-sided polygon total (2n - 4 right angles or 180n - 360 degrees

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Interior angles and if it has more than 3 sides also diagonals

No, but the diagonals of a square does bisects its interior angles.

A polygon with all interior angles congruent Is known as a regular polygon.

If all of its interior angles are equal then it is a regular polygon

Suppose the polygon has V vertices.Then sum of interior angles is (V - 2)*180 degrees = 1980 degrees => V - 2 = 1980/180 = 11 => V = 13 A polygon with V vertices has V*(V-3)/2 = 13*10/2 = 65 diagonals.

If the polygon has n sides, the sum of its interior angles is 180*(n - 2) degrees. [Whether the polygon is regular or not is irrelevant] So, 180*(n - 2) = 1080 (n - 2) = 6 n = 8 Then number of diagonals = n*(n - 3)/2 = 8*5/2 = 20

By drawing all the diagonals from one vertex, the polygon is divided up into triangles. The sum of the interior angles of the polygon is equal to the sum of the internal angles in the triangles. With n vertices, each vertex is not directly connected to n-3 other vertices, thus n-3 diagonals can be drawn from a vertex which will create n-2 triangles (each with the sum of their interior angles as 180o); so: sum_of_interior_angles = 180 x (number_of_sides - 2)

Yes. The interior angles of a polygon add up to 360°.

Any polygon can have two interior angles of 12 degrees. No polygon can have all its interior angles of 12 degrees.

Interior angles of n-sided polygon total (2n - 4) right angles or 180n - 360 degrees.

Interior angles of n-sided polygon total (2n - 4) right angles or 180n - 360 degrees.

The smallest regular polygon, an equilateral triangle, has interior angles of 60. A square has interior angles of 90. There can't exist a regular polygon with interior angles of 30.

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