Question

Знайдіть кути трикутника якщо зовнішні кути трикутника пропорційні числам 5 6 7

Answer 1

Нехай один кут 5х, тоді другий 6х, третій 7х,
Сума кутів трикутника дорівнює 180 градусів, отже
5х+6х+7х=180
18х=180
х=10

5х=5*10=50
6х=60
7х=70
Відповідь: 50 градусів, 60 градусів, 70 градусів!

Answer 2

Finding the Angles of a Triangle with Proportional External Angles

To find the angles of a triangle when the external angles are proportional to the numbers 5, 6, and 7, we can use the fact that the sum of the measures of the exterior angles of any polygon is always 360 degrees.

Given that the external angles are in the ratio of 5:6:7, we can calculate the measures of the individual external angles using the proportion and then find the corresponding internal angles of the triangle.

Let's proceed with the calculations:

1. Calculating the Measures of the External Angles: - Let's assume the external angles of the triangle are 5x, 6x, and 7x, where x is a constant. - According to the given ratio, the sum of the measures of the external angles is 5x + 6x + 7x = 360 degrees. - Solving for x: - 5x + 6x + 7x = 360 - 18x = 360 - x = 20

2. Finding the Measures of the Individual External Angles: - Now that we have the value of x, we can find the measures of the individual external angles: - 5x = 5 * 20 = 100 degrees - 6x = 6 * 20 = 120 degrees - 7x = 7 * 20 = 140 degrees

3. Calculating the Internal Angles of the Triangle: - The sum of the internal angles of a triangle is always 180 degrees. - Using the fact that the exterior angle and the interior angle at a vertex are supplementary, we can find the measures of the internal angles: - The internal angle corresponding to the 100-degree external angle is 180 - 100 = 80 degrees. - The internal angle corresponding to the 120-degree external angle is 180 - 120 = 60 degrees. - The internal angle corresponding to the 140-degree external angle is 180 - 140 = 40 degrees.

Therefore, the angles of the triangle with external angles proportional to the numbers 5, 6, and 7 are: - 80 degrees, 60 degrees, and 40 degrees.