What is the angle sum of a polygon with 9 sides?

kemecryncqe9

kemecryncqe9

Answered question

2022-11-09

What is the angle sum of a polygon with 9 sides?

Answer & Explanation

Aedan Hatfield

Aedan Hatfield

Beginner2022-11-10Added 16 answers

Step 1
A nonagon can have 6 diagonals drawn inside of it to form 7 interior triangles.
Every triangle's angles have a sum of 180 ˚ . Therefore, since there are 7 triangles, the sum of the interior angles in a nine-sided polygon is
7 × 180 ˚ = 1260 ˚
This can be generalized to a polygon with n sides, since n - 2 triangles can be drawn in any polygon. Thus, the formula is
180 ˚ ( n - 2 )

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