Question

В равнобедренном трегульнике ABC с основанием AC внешний угол при вершине С равен 123 градуса Найдите велечину угла BAC.Ответ дайте в градусах Помогите

Answer 1

Finding the Angle BAC in an Isosceles Triangle

To find the measure of angle BAC in an isosceles triangle ABC with base AC and an external angle of 123 degrees at vertex C, we can use the fact that the sum of the angles in a triangle is always 180 degrees.

Let's denote the measure of angle BAC as x.

According to the given information, the external angle at vertex C is 123 degrees. An external angle is equal to the sum of the two opposite interior angles. Therefore, we can write the equation:

x + x = 123

Simplifying the equation, we have:

2x = 123

To solve for x, we divide both sides of the equation by 2:

x = 123 / 2

Calculating the value of x, we get:

x = 61.5 degrees

Therefore, the measure of angle BAC is 61.5 degrees.

Conclusion

In an isosceles triangle ABC with base AC and an external angle of 123 degrees at vertex C, the measure of angle BAC is 61.5 degrees.