Question

Чему равен внутренний угол правильного многоугольника у которого 9 диагоналей? ответ в градусах

Answer 1

В многоугольнике n(n-3)/2 диагоналей, по условию это 9
n(n-3)/2=9
n(n-3)=18
n²-3n-18=0
D=9+72=81
n=-3 - не подходит n=6 - подходит)), значит у нас шестиугольник.
Внутренний угол правильного многоугольника равен 180⁰(n-2)/n=
=180⁰(6-2)/6=120°

Answer 2

Calculating the Interior Angle of a Regular Polygon with 9 Diagonals

To calculate the interior angle of a regular polygon with 9 diagonals, we can use the formula:

Interior Angle = (180 * (n - 2)) / n

Where: - n is the number of sides of the polygon.

Using this formula, we can calculate the interior angle for the given polygon with 9 diagonals.

Calculation

Using the formula, we can calculate the interior angle for the polygon with 9 diagonals:

Interior Angle = (180 * (9 - 2)) / 9

Interior Angle = (180 * 7) / 9

Interior Angle ≈ 140 degrees

Therefore, the interior angle of the regular polygon with 9 diagonals is approximately 140 degrees.