Question

Вася вырезал из картона треугольник и пронумеровал его вершины цифрами 1, 2, 3. Оказалось, что если Васин треугольник повернуть 24 раза по часовой стрелке вокруг его вершины под номером 1 на угол, равный углу при этой вершине, то он вернется в исходное положение. Если Васин треугольник повернуть 8 раз по часовой стрелке вокруг его вершины под номером 2 на угол, равный углу при этой вершине, то он вернется в исходное положение. Вася утверждает, что если повернуть его треугольник праз вокруг вершины под номером 3 на угол, равный углу при этой вершине, то он вернется в исходное положение. Какое минимальное п мог назвать Вася так, чтобы его утверждение было правдивым хотя бы для какого-то картонного треугольника?​

Answer 1

Ответ:6

Пошаговое объяснение:

Answer 2

Ответ:

3

Пошаговое объяснение:

3 угол должен быть максимальным поэтому 1уг = 360\ 24= 15

2уг = 360\8=45

3уг = 120

360\120=3

Answer 3

To solve this problem, let's analyze the given information step by step.

Vasya cut out a triangle from cardboard and numbered its vertices with the digits 1, 2, and 3. He found that if he rotated the triangle 24 times clockwise around vertex number 1 by an angle equal to the angle at that vertex, it would return to its original position. Similarly, if he rotated the triangle 8 times clockwise around vertex number 2 by an angle equal to the angle at that vertex, it would also return to its original position. Vasya claims that if he rotates the triangle p times clockwise around vertex number 3 by an angle equal to the angle at that vertex, it will also return to its original position.

To find the minimum value of p that makes Vasya's claim true, we need to determine the angle at vertex number 3.

Let's denote the angles at vertices 1, 2, and 3 as A, B, and C, respectively.

Since the triangle returns to its original position after 24 rotations around vertex number 1, we can write the equation:

24A = 360 degrees

Simplifying the equation, we find:

A = 15 degrees

Similarly, since the triangle returns to its original position after 8 rotations around vertex number 2, we can write the equation:

8B = 360 degrees

Simplifying the equation, we find:

B = 45 degrees

Now, let's consider the rotation around vertex number 3. We want to find the minimum value of p that satisfies the equation:

pC = 360 degrees

To find the minimum value of p, we need to find the smallest angle C that satisfies the equation. Since the sum of the angles in a triangle is always 180 degrees, we can write:

A + B + C = 180 degrees

Substituting the values of A and B, we have:

15 + 45 + C = 180

Simplifying the equation, we find:

C = 120 degrees

Now, we can substitute the value of C into the equation for the rotation around vertex number 3:

p * 120 = 360

Simplifying the equation, we find:

p = 3

Therefore, the minimum value of p that Vasya can name to make his claim true is 3. If he rotates the triangle 3 times clockwise around vertex number 3 by an angle equal to the angle at that vertex (120 degrees), the triangle will return to its original position.

Please let me know if you need any further clarification.