Question

БИССЕКТРИСА ВНЕШНЕГО УГЛА ПРИ ВЕРШИНЕ В ТРЕУГОЛЬНИКА ABC ПАРАЛЛЕЛЬНА СТОРОНЕ AC. Найдите величину угла CAB,если угол ABC=30 градусов.Ответ дайте в градусах

Answer 1

Ответ:

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Answer 2

Bisector of an External Angle in Triangle ABC

To find the measure of angle CAB in triangle ABC, given that angle ABC is 30 degrees and the bisector of the external angle at vertex A is parallel to side AC, we can use the angle bisector theorem.

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

Let's denote the length of segment CA as x and the length of segment CB as y. According to the angle bisector theorem, we have the following proportion:

CA / CB = BA / BC Since the bisector of the external angle at vertex A is parallel to side AC, we can also conclude that angle CAB is equal to angle ABC. Therefore, angle CAB is also 30 degrees.

So, the measure of angle CAB is 30 degrees.