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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

Q: If the sum of interior angles a regular polygon is 1080 degrees how many diagonals does this polygon have?

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If it is a regular polygon with each interior angle of 120 degrees then it is an hexagon which will have 0.5((6^2)-3*6) equals 9 diagonals

The interior angles of a regular polygon must be 60 degrees or greater.

The only regular polygon with an interior angle of 90 degrees is the square, which has four sides. Other polygons can have an interior angle of 90 degrees, but they would not be regular polygons.

Exterior angle: 180-157.5 = 22.5 degrees Number of sides: 360/22.5 = 16 Using the diagonal formula: 0.5*(162-48) = 104 diagonals

If it's a regular polygon then each interior angle measures 120 degrees.

Related questions

If it is a regular polygon with each interior angle of 120 degrees then it is an hexagon which will have 0.5((6^2)-3*6) equals 9 diagonals

No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more. No regular polygon can have an interior angle of 180 degrees or more.

It has 180 sides if the interior of the (regular) polygon has a total of 178 'degrees'.

The interior angles of a regular polygon must be 60 degrees or greater.

The only regular polygon with an interior angle of 90 degrees is the square, which has four sides. Other polygons can have an interior angle of 90 degrees, but they would not be regular polygons.

Obtuse

Exterior angle: 180-157.5 = 22.5 degrees Number of sides: 360/22.5 = 16 Using the diagonal formula: 0.5*(162-48) = 104 diagonals

If it's a regular polygon then each interior angle measures 120 degrees.

13 1/3 °

It cannot be a regular polygon with interior angles of 24 degrees since the smallest interior angle in a regular polygon is 60 degrees. If it is an irregular polygon, then any one of them, with 3 or more sides, can have an angle of 24 degrees.

The interior angles of a 15 sided polygon add up to 2340 degrees and if it is a regular polygon then each interior angle is 156 degrees.

A nonagon is a 9 sided polygon which can be regular or irregular Its 9 interior angles add up to 1260 degrees It has 27 diagonals