Question

отрезок DM биссектриса треугольника CDE через точку M проведена Прямая параллельная стороне CD и пересекающая сторону de в точке N Найдите углы треугольника dmn если угол CDE равен 76 градусов​

Answer 1

Ответ:

Угол МDN =38

Угол MND=104

Угол М=38

Объяснение:

На фото

Answer 2

Problem Analysis

We are given a triangle CDE, and a line segment DM that bisects the triangle through point M. Another line is drawn parallel to side CD and intersects side DE at point N. We need to find the angles of triangle DMN given that angle CDE is 76 degrees.

Solution

To find the angles of triangle DMN, we can use the properties of parallel lines and the angle bisector theorem.

Let's start by labeling the angles of triangle DMN as follows: - Angle DMN = x - Angle DNM = y - Angle MND = z

Since line DM bisects triangle CDE, we know that angle CDM is equal to angle MDE. Let's denote this angle as a.

Using the angle bisector theorem, we can set up the following proportion: CD/CE = DM/ME

Since line DM is parallel to side CD, we can use the alternate interior angles theorem to conclude that angle CDM is equal to angle DMN. Let's denote this angle as b.

Using the angle bisector theorem again, we can set up the following proportion: CD/CE = DN/NE

Now, let's solve for the angles of triangle DMN.

Angle x:

Since angle CDM is equal to angle DMN, we can substitute angle a for angle CDM in the proportion: CD/CE = DM/ME

Simplifying the proportion, we get: CD/CE = DM/ME CD/CE = DM/(DM + ME) CD/CE = DM/(DM + DN)

Since line DM is parallel to side CD, we can use the alternate interior angles theorem to conclude that angle CDE is equal to angle DMN. Let's denote this angle as c.

Substituting the given angle CDE (76 degrees) and angle a (CDM) into the proportion, we get: CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM + DN) CD/CE = DM/(DM