Question

AD параллельно BC угол ACB равен 50 градусов AC-биссектриса угла BAD Найти: угол ABC

Answer 1

ACB=CAD=50град.(как накрест лежащие); CAD=CAB=50град.(AC - биссектриса); АВС=180гр-50гр-50гр=80гр. Ответ: угол ABC равен 80 градусов.

Answer 2

Given Information:

We are given that in triangle ABC, AD is parallel to BC, and angle ACB is equal to 50 degrees. We are also told that AC is the angle bisector of angle BAD. We need to find the measure of angle ABC.

Solution:

To find the measure of angle ABC, we can use the angle bisector theorem. According to the angle bisector theorem, the ratio of the lengths of the two segments created by the angle bisector is equal to the ratio of the lengths of the two opposite sides of the triangle.

In triangle ABC, AC is the angle bisector of angle BAD. Therefore, we can apply the angle bisector theorem to find the relationship between the lengths of the segments created by AC.

Let's denote the length of segment AD as x and the length of segment BD as y. Then, according to the angle bisector theorem:

AD/BD = AC/BC Since AD is parallel to BC, we can also apply the alternate interior angles theorem to conclude that angle ABC is equal to angle BDA. Therefore, we can rewrite the equation as:

AD/BD = AC/CD Now, let's substitute the given information into the equation. We know that angle ACB is equal to 50 degrees, so angle BCD is also equal to 50 degrees. Therefore, angle ABC is equal to 180 - 50 - 50 = 80 degrees.

Hence, the measure of angle ABC is 80 degrees.

Summary:

In triangle ABC, with AD parallel to BC and angle ACB equal to 50 degrees, and AC being the angle bisector of angle BAD, the measure of angle ABC is 80 degrees.