Question

Как изменится сумма углов высокого многоугольника , если количество сторон увеличится на 3

Answer 1

Сумма внутренних углов многоугольника вычисляется по формуле
∑ = 180°(n - 2), где n - количество сторон многоугольника
Количество сторон увеличили на 3 :  N = n+3
∑₁ = 180°(N - 2) = 180°(n - 2 + 3) = 180°(n - 2)+3*180°
∑₁ = 180°(n - 2) + 540°

Сумма внутренних углов увеличится на 540°

Answer 2

Calculating the Sum of Angles in a Polygon

When the number of sides in a polygon increases by 3, the sum of the interior angles of the polygon changes. The formula to calculate the sum of the interior angles of a polygon is given by:

Sum of Interior Angles = (n - 2) * 180 degrees

Where: - n = number of sides in the polygon

Change in the Sum of Angles

When the number of sides in a polygon increases by 3, the change in the sum of the interior angles can be calculated using the formula:

New Sum of Interior Angles = (n + 3 - 2) * 180 degrees

Simplifying the equation: New Sum of Interior Angles = (n + 1) * 180 degrees

Therefore, when the number of sides in a polygon increases by 3, the sum of the interior angles will increase by 180 degrees.

This information is supported by the general formula for the sum of interior angles in a polygon and does not require external sources for verification.