Question

один із зовнішніх кутів трикутника дорівнює 120⁰ знайдіть внутрішні кути не суміжні з ними якщо вони відносяться 3:7​

Answer 1

Ответ:

36, 84

Объяснение:

Нехай К коєфіціент пропорційності, тоді

3k+7k=120 (два несуміжні кути з зовнішнім= зовнішньому куту)

10к=120

К=120:10

К=12

1) 12*3=36

2) 12*7=84

Answer 2

Finding the Non-Adjacent Interior Angles of a Triangle

To find the non-adjacent interior angles of a triangle when one of the exterior angles is 120 degrees, we can use the fact that the sum of the exterior angles of any polygon is always 360 degrees.

Given that one of the exterior angles is 120 degrees, we can find the corresponding interior angle by subtracting the exterior angle from 180 degrees. This is based on the property that the exterior angle and the interior angle it corresponds to are supplementary, meaning they add up to 180 degrees.

Calculation

Let's denote the non-adjacent interior angles as x and y. The exterior angle is 120 degrees.

We know that: - The sum of all exterior angles of any polygon is 360 degrees. - The exterior angle and the interior angle it corresponds to are supplementary.

So, we can set up the equation: x + 120 + y = 360

We also know that the non-adjacent interior angles are in the ratio 3:7. This means we can express one of the angles in terms of the other using this ratio.

Let's denote one of the angles as 3k and the other as 7k, where k is a constant.

We can now solve for x and y using the equation and the ratio.

Solution

Using the equation x + 120 + y = 360 and the ratio 3:7, we can solve for the non-adjacent interior angles.

First, we express one angle in terms of the other using the ratio: x = 3k y = 7k

Substitute these into the equation: 3k + 120 + 7k = 360 10k + 120 = 360 10k = 240 k = 24

Now we can find the values of x and y: x = 3k = 3 * 24 = 72 y = 7k = 7 * 24 = 168

So, the non-adjacent interior angles are: x = 72 degrees y = 168 degrees