Question

Два внешних угла треугольника 120 градусов и 160 градусов. Найдите его третий внешний угол. Сделайте вывод о сумме внешних углов треугольника.Пожалуйста решите. Мне завтра утром нужно это сдать!

Answer 1

3 угол равен 80 градусам. Так как сумма внешних углов треугольника равно 360 градусов. 360-(120+160)=80(градусов).

   Вывод: сумма внешних углов треугольника в 2 раза больше сумме внутренних углов треугольника!

Answer 2

Finding the Third Exterior Angle of a Triangle

To find the third exterior angle of a triangle, we can use the fact that the sum of the measures of the exterior angles of any triangle is always 360 degrees.

Let's denote the three exterior angles of the triangle as A, B, and C. We are given that the measures of two of the exterior angles are 120 degrees and 160 degrees.

To find the measure of the third exterior angle, we can subtract the sum of the measures of the two given exterior angles from 360 degrees:

Third Exterior Angle = 360 degrees - (120 degrees + 160 degrees)

Calculating this expression, we get:

Third Exterior Angle = 360 degrees - 280 degrees = 80 degrees

Therefore, the measure of the third exterior angle of the triangle is 80 degrees.

Sum of Exterior Angles of a Triangle

The sum of the measures of the exterior angles of any triangle is always 360 degrees. This means that if we add up the measures of all three exterior angles of a triangle, the result will always be 360 degrees.

In this case, the sum of the measures of the three exterior angles of the triangle is:

120 degrees + 160 degrees + 80 degrees = 360 degrees

Therefore, the sum of the exterior angles of the triangle is 360 degrees, which confirms the general rule for all triangles.

I hope this helps! Let me know if you have any further questions.