Question

Кто ответить получить 30 баллов. Если ответ без обьяснения-бан.Если ответь неправильный-БАН. Якими є кути трикутника, якщо зовнішні кути співвідносяться як 3:4:2? Напишите условия и решите

Answer 1

Сума зовнішніх кутів трикутника, взятих по одному при кожній вершині, дорівнює 360°.

Знайдемо коефіціент пропорційності х з рівняння:

3х+4х+2х=360

9х=360

х=40

Міра зовнішніх кутів: 40*3=120°;  40*4=160°;  40*2=80°

Міри внутрішніх кутів: ∠1=180-120=60°;  ∠2=180-160=20°;  ∠3=180-80=100°

Answer 2

Пусть х - коэф-нт пропорциональности.

Сумма смежных углов = 180гр., сумма трёх внешних углов = 360гр. Исходя из этого, составим ур-е:

3х+4х+2х=360

9х=360

х=40гр.

Значит, внешние углы треугольника: 40*4=160гр., 40*3=120гр., 40*2=80гр.

А чтобы найти углы самого треугольника, вычитаем из 180гр. эти значения. Углы треугольника: 20, 60, 100.

Answer 3

Triangle Angle Ratios

To determine the angles of a triangle when the external angles are in a ratio of 3:4:2, we need to understand the relationship between the internal and external angles of a triangle.

In any triangle, the sum of the internal angles is always 180 degrees. The external angle at a vertex is equal to the sum of the two non-adjacent internal angles at that vertex.

Let's assume the external angles of the triangle are in the ratio of 3:4:2. We can assign variables to these ratios, such as 3x, 4x, and 2x, where x is a constant.

Now, we can set up equations to find the values of x and the internal angles of the triangle.

The external angles are related to the internal angles as follows:

External Angle 1 = Internal Angle 1 + Internal Angle 2 External Angle 2 = Internal Angle 2 + Internal Angle 3 External Angle 3 = Internal Angle 3 + Internal Angle 1

Using the ratios we have, we can substitute the values:

3x = Internal Angle 1 + Internal Angle 2 4x = Internal Angle 2 + Internal Angle 3 2x = Internal Angle 3 + Internal Angle 1

To solve these equations, we can use a system of equations or algebraic manipulation. Let's use algebraic manipulation to find the values of x and the internal angles.

Adding the three equations together, we get:

3x + 4x + 2x = (Internal Angle 1 + Internal Angle 2) + (Internal Angle 2 + Internal Angle 3) + (Internal Angle 3 + Internal Angle 1)

Simplifying the equation:

9x = 2(Internal Angle 1 + Internal Angle 2 + Internal Angle 3)

Since the sum of the internal angles is always 180 degrees, we can substitute this value:

9x = 2(180) 9x = 360 x = 40

Now that we have the value of x, we can find the internal angles:

Internal Angle 1 = 3x = 3(40) = 120 degrees Internal Angle 2 = 4x = 4(40) = 160 degrees Internal Angle 3 = 2x = 2(40) = 80 degrees

Therefore, the angles of the triangle, when the external angles are in a ratio of 3:4:2, are 120 degrees, 160 degrees, and 80 degrees.

Note: It's important to verify the information provided above with additional sources to ensure accuracy.