Question

Отрезки AK и BM - биссектрисы равнобедренного треугольника ABC, AC - основание. Биссектрисы пересекаются в точке О. KOB=70 градусов. Найдите градусную меру угла C треугольника ABC. Помогите плиз!!! Срочно надо

Answer 1

Углы KOB и AOM - вертикальные, а следовательно равны. То есть угол AOM = 70 градусов.
Рассмотрим треугольник АОМ. ВМ является и высотой, значит угол ОМА = 90 градусов. Угол ОАМ = 90 - угол АОМ = 90 - 70 = 20.
Так как АК - биссектрисса, то угол ВАО = углу ОАМ = 20 градусов. Значит угол ВАС = ВАО + ОАМ = 20 + 20 = 40 градусов. Так как треугольник АВС - равнобедренный, то угол С = углу В = 40 градусов.
Ответ: 40 градусов.

Answer 2

Solving for Angle C in Triangle ABC

To find the degree measure of angle C in triangle ABC, given that segments AK and BM are the bisectors of isosceles triangle ABC, and AC is the base, we can use the information provided.

First, let's establish the given information: - Segments AK and BM are the bisectors of isosceles triangle ABC. - AC is the base of the isosceles triangle. - The bisectors intersect at point O, and ∠KOB = 70 degrees.

Solution Steps

1. Identifying the Properties of Isosceles Triangle: - In an isosceles triangle, the bisectors of the base angles are also the altitudes and medians. - The bisectors of the base angles are also the angle bisectors.

2. Using the Properties of Isosceles Triangle: - Since AK and BM are the bisectors of the base angles of the isosceles triangle ABC, they are also the angle bisectors. - The angle bisectors of a triangle intersect at the incenter of the triangle, which is equidistant from the sides of the triangle.

3. Finding Angle C: - The angle bisectors intersect at the incenter of the triangle, which is equidistant from the sides of the triangle. - Therefore, ∠KOC = ∠BOC = 70 degrees (as given). - Since ∠KOC and ∠BOC are equal, they each measure half of angle C.

4. Calculating Angle C: - To find the measure of angle C, we can use the fact that the sum of the angles in a triangle is 180 degrees. - Therefore, angle C = 2 * ∠KOC = 2 * 70 degrees = 140 degrees.

Conclusion

The degree measure of angle C in triangle ABC is 140 degrees.