Question

Скільки вершин має опуклий многокутник,якщо два його кути дорівнюють по 120 градусів,а інші - по 100 градусів?

Answer 1

Сумма углов n-угольника равна 180°(n-2)

Сумма углов нашего n-угольника 120 * 2 + 100 * ( n-2)

приравняем 180°(n-2) = 120 * 2 + 100 * ( n-2)  решим уравнение

240 = 180(n-2) - 100 * ( n-2)

240 = (n-2) * (180 - 100)

n-2 = 240 / 80

n-2 = 3

n = 3 + 2

n = 5

 

Ответ: n-угольник имеет 5 вершин (пятиугольник)

 

проверка 180 (5 - 2) = 540

120 * 2 + 100 * 3 = 540

Answer 2

Number of Vertices in Convex Polygon

A convex polygon with two angles measuring 120 degrees and the remaining angles measuring 100 degrees each has a specific number of vertices.

The sum of the interior angles of a polygon can be calculated using the formula: Sum of interior angles = (n - 2) * 180 degrees, where n is the number of sides (or vertices) of the polygon.

Calculation

Using the given information, we can calculate the number of sides (n) of the polygon: - Two angles of 120 degrees each - Remaining angles of 100 degrees each

Let's solve for the number of sides (n) using the formula: (n - 2) * 180 = 120 * 2 + 100 * (n - 2)

Solving for n: (n - 2) * 180 = 240 + 100n - 200 180n - 360 = 100n + 40 80n = 400 n = 5

Conclusion

Therefore, the convex polygon in question has 5 vertices.