Question

Внутренние углы треугольника пропорциональны числам 2,5,8. Найдите меньший угол треугольника. Ответ дайте в градусах. 50 БАЛЛОВ ПОМОГИТЕ ПОЖАЛУЙСТА

Answer 1

Отношение углов равно: 2:5:8.

А сумма углов в треугольнике равна 180 градусам, тоесть — составим уравнение с одной переменной "x":

$2x+5x+8x = 180^o\\15x = 180^o\\x = 180/15 = 12^o\\2x = 12*2 = 24^o.$

Самый меньший угол — переменная с коэффициентом 2, которая равна: 24°.

Вывод: Самый меньший угол равен 24°.

Answer 2

Finding the Smallest Angle of a Triangle

To find the smallest angle of a triangle when the internal angles are proportional to the numbers 2, 5, and 8, we can use the fact that the sum of the internal angles of a triangle is always 180 degrees.

Let's assume that the three internal angles of the triangle are 2x, 5x, and 8x, where x is a constant. Since the sum of the internal angles is 180 degrees, we can set up the following equation:

2x + 5x + 8x = 180

Simplifying the equation, we get:

15x = 180

Dividing both sides of the equation by 15, we find:

x = 12

Now that we know the value of x, we can find the measure of each angle:

- The smallest angle is 2x = 2 * 12 = 24 degrees. - The second angle is 5x = 5 * 12 = 60 degrees. - The largest angle is 8x = 8 * 12 = 96 degrees.

Therefore, the smallest angle of the triangle is 24 degrees.

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