Question

В треугольнике АВС проведена медиана АМ, АМ=ВМ, угол АСВ =62 градусамнайдите величину угла МВА

Answer 1

AMC-равнобедренный, ВМ=МС=АМ по условию, значит угол МАС равен 62,угол АМС 56. Смежный с ним АМВ равен 124. Треугольник АМВ тоже равнобедренный, углы при основании равны, угол МВА=(180-124):2=56:2=28

Answer 2

Problem Analysis

We are given a triangle ABC with a median AM, where AM = VM, and angle ASB is 62 degrees. We need to find the measure of angle MVA.

Solution

To find the measure of angle MVA, we can use the fact that the medians of a triangle divide each other into segments of equal length. This means that AM = VM.

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

Since AM = VM, we can also say that angle AMV = angle VMA = x.

Now, let's consider triangle AMV. The sum of the angles in a triangle is always 180 degrees. So, we can write the following equation:

x + x + 62 = 180

Simplifying the equation, we get:

2x + 62 = 180

Subtracting 62 from both sides, we have:

2x = 180 - 62 2x = 118

Dividing both sides by 2, we get:

x = 118 / 2 x = 59

Therefore, the measure of angle MVA is 59 degrees.

Conclusion

In triangle ABC, with a median AM where AM = VM and angle ASB is 62 degrees, the measure of angle MVA is 59 degrees.