Question

на одной из сторон угла ABC отметили точку D, через которую провели прямую, параллельную BC. эта прямая пересекает биссектрису угла ABC в точке M. найдите углы треугольника BDM, если угол ABC равен 70 градусов. СРОЧНО ПОЖАЛУЙСТА!!!!

Answer 1

Given Information:

We are given a triangle ABC, where angle ABC is 70 degrees. Point D is marked on one side of angle ABC, and a line parallel to BC is drawn through point D. This line intersects the angle bisector of angle ABC at point M. We need to find the angles of triangle BDM.

Solution:

To find the angles of triangle BDM, we can use the given information and some geometric properties.

Let's analyze the given information step by step:

1. Angle ABC is given as 70 degrees. 2. Point D is marked on one side of angle ABC, and a line parallel to BC is drawn through point D. This means that angle BDC is also 70 degrees, as it is corresponding to angle ABC. 3. The line parallel to BC intersects the angle bisector of angle ABC at point M. This means that angle MBC is equal to angle ABC, which is 70 degrees.

Now, let's find the angles of triangle BDM:

1. Angle BDM: Angle BDM is formed by the lines BD and DM. We know that angle BDC is 70 degrees, and angle MBC is also 70 degrees. Therefore, angle BDM can be found by subtracting the sum of angles BDC and MBC from 180 degrees: Angle BDM = 180 degrees - (angle BDC + angle MBC) = 180 degrees - (70 degrees + 70 degrees) = 180 degrees - 140 degrees = 40 degrees

2. Angle DBM: Angle DBM is formed by the lines DB and BM. We know that angle BDM is 40 degrees, and angle MBC is 70 degrees. Therefore, angle DBM can be found by subtracting the sum of angles BDM and MBC from 180 degrees: Angle DBM = 180 degrees - (angle BDM + angle MBC) = 180 degrees - (40 degrees + 70 degrees) = 180 degrees - 110 degrees = 70 degrees

3. Angle MDB: Angle MDB is formed by the lines MD and DB. We know that angle DBM is 70 degrees, and angle BDM is 40 degrees. Therefore, angle MDB can be found by subtracting the sum of angles DBM and BDM from 180 degrees: Angle MDB = 180 degrees - (angle DBM + angle BDM) = 180 degrees - (70 degrees + 40 degrees) = 180 degrees - 110 degrees = 70 degrees

Therefore, the angles of triangle BDM are as follows: - Angle BDM = 40 degrees - Angle DBM = 70 degrees - Angle MDB = 70 degrees

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