Question

На прямой АВ взята точка М,луч МD является бесиктрисой угла СМВ,найдите чему равен угол АМD,если угол DМС равен 57° Ответьте пожалуйста

Answer 1

Ответ:

66

Пошаговое объяснение:

т.к. луч МD является бесиктрисой угла СМВ, угол СМВ=2 угла DMC =114 гр

угол АМD = 180-114=66гр (смежные углы)

Answer 2

Given Information:

- Point M lies on line segment AB. - Ray MD is the angle bisector of angle CMV. - Angle DMC is 57°.

To Find:

The measure of angle AMD.

Solution:

To find the measure of angle AMD, we need to use the angle bisector theorem. According to this theorem, the angle bisector of an angle divides the opposite side into two segments that are proportional to the other two sides of the triangle.

In this case, we have angle CMV, and the angle bisector MD divides side CV into two segments, CM and MV. Let's denote the length of CM as x and the length of MV as y.

Using the angle bisector theorem, we can set up the following proportion:

CM/MV = CV/VB

Since CM and MV are equal in length (as they are the same segment), we can rewrite the proportion as:

x/y = CV/VB

Now, let's substitute the given information into the proportion. We know that angle DMC is 57°, so angle CMV is twice that, which is 114°. We also know that angle AMV is equal to angle CMV because MD is the angle bisector. Therefore, angle AMV is also 114°.

Since angle AMV and angle AMD are adjacent angles, their measures add up to 180°. So we can write the equation:

AMV + AMD = 180°

Substituting the known values:

114° + AMD = 180°

Now we can solve for AMD:

AMD = 180° - 114°

AMD = 66°

Therefore, the measure of angle AMD is 66°.