Question

Биссектрисы углов A и C треугольника ABC пересекаются в точке О Найдите угол ABC если угол АОС равен 125 градусов​

Answer 1

Ответ:

1) <OAC + <OCA = 180°-125° = 55°

2) <ABC = 180° - (55°×2) = 70°

Ответ: <ABC = 70°

Answer 2

Finding Angle ABC

To find the angle ABC in triangle ABC, given that angle AOC is 125 degrees, we can use the angle bisector theorem. According to the theorem, the angle bisector of angle A divides the side BC into two segments that are proportional to the other two sides of the triangle.

Using the Angle Bisector Theorem

The angle bisector theorem states that if a ray bisects an angle of a triangle, it divides the opposite side into segments that are proportional to the other two sides of the triangle.

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

AC/AB = OC/OB

Where OC and OB are the lengths of the segments created by the angle bisector at point O.

Applying the Theorem to Find Angle ABC

Given that angle AOC is 125 degrees, we can use this information to find the ratio of the lengths of the segments AC and AB. Then, we can use this ratio to find the measure of angle ABC.

Let's denote the measure of angle ABC as "x".

Using the angle bisector theorem, we have:

AC/AB = OC/OB

Now, we can use the fact that angle AOC is 125 degrees to find the ratio of the lengths of the segments AC and AB.

Calculation

Using the given angle AOC = 125 degrees, we can calculate the ratio of the lengths of the segments AC and AB and then use this ratio to find the measure of angle ABC.

Let's proceed with the calculation.