Question

Найти углы треугольника если его внешние углы пропорциональны числам 5 6 и 7​

Answer 1

Объяснение:

5+6+7=18

180°:18=10°

10°×5=50°

10°×6=16°

10°×7=70°

это если нужно найти градусы этих углов

5+6+7=18

18-5=13

18-6=12

18-7=11

а это если нужно найти их пропорции к друг другу

Answer 2

Finding the Angles of a Triangle with Proportional External Angles

To find the angles of a triangle when its external angles are proportional to the numbers 5, 6, and 7, we can use the fact that the sum of an angle and its corresponding external angle is 180 degrees. Let's denote the three external angles as A, B, and C, and the corresponding internal angles as A', B', and C'. Then we have the following relationships:

1. A + A' = 180 2. B + B' = 180 3. C + C' = 180

Given that the external angles are proportional to 5, 6, and 7, we can express them as 5x, 6x, and 7x, where x is a constant.

Now, we can solve for the internal angles using the given proportions.

Step 1: Set up the proportions for the external angles: - A' = 5x - B' = 6x - C' = 7x

Step 2: Use the fact that the sum of an angle and its corresponding external angle is 180 degrees to find the internal angles: - A + 5x = 180 - B + 6x = 180 - C + 7x = 180

Step 3: Solve for the internal angles A, B, and C: - A = 180 - 5x - B = 180 - 6x - C = 180 - 7x

By substituting the given proportional values (5x, 6x, and 7x) into the equations, we can find the specific angles A, B, and C.

This method allows us to find the angles of the triangle when the external angles are proportional to the given numbers.

I hope this helps! If you have any further questions or need additional assistance, feel free to ask.