Question

АВС равнобедренный с основанием АС. Из углов А и В проведены биссектрисы, которые при пересечении образуют угол 100 градусов. Найти углы треуг АВС

Answer 1

Вобщем, 20, 20 и 140

Answer 2

Problem Analysis

We are given a triangle ABC, where AB = AC, and the bisectors of angles A and B intersect at an angle of 100 degrees. We need to find the measures of angles A, B, and C.

Solution

Let's analyze the given information step by step to find the measures of angles A, B, and C.

1. We are given that triangle ABC is an isosceles triangle with AB = AC. This means that angles A and C are congruent.

2. The bisectors of angles A and B intersect at an angle of 100 degrees. Let's call the point of intersection of the bisectors O.

3. Since the bisectors of angles A and B intersect at O, angle AOC is 100 degrees.

4. Since triangle ABC is isosceles, angles A and C are congruent. Let's call the measure of angles A and C as x.

5. Therefore, angle AOC is equal to 2x (since it is the sum of angles A and C).

6. We know that angle AOC is 100 degrees, so we can write the equation: 2x = 100.

7. Solving the equation, we find that x = 50.

8. Since angles A and C are congruent, both angles A and C measure 50 degrees.

9. Angle B is the remaining angle in triangle ABC. Since the sum of angles in a triangle is 180 degrees, we can find angle B by subtracting the sum of angles A and C from 180 degrees.

10. Angle B = 180 - (angle A + angle C) = 180 - (50 + 50) = 180 - 100 = 80 degrees.

Therefore, the measures of angles A, B, and C in triangle ABC are: - Angle A = 50 degrees - Angle B = 80 degrees - Angle C = 50 degrees

Note: The information provided in the search results did not directly answer the question. However, the solution can be derived using basic properties of triangles and angle bisectors.