Question

В треугольнике ABC угол A = 54 градуса, угол B = 82 градуса, AL,BN и CK - биссектрисы, пересекающиеся в точке О.Найдите угол AOK. ответ в градусах

Answer 1

расмотрим треуг АСК

С=(180-54-82):2=22

А=54

К=104

Расмотрим треуг.АОК

А=27

К=104

О=49 

Answer 2

Triangle ABC and Bisectors

In triangle ABC, angle A = 54 degrees, angle B = 82 degrees, and AL, BN, and CK are the angle bisectors intersecting at point O.

Finding Angle AOK

To find the angle AOK, we can use the angle bisector theorem, which states that in a triangle, an angle bisector divides the opposite side in a ratio of the adjacent sides. Let's denote the angles as follows: - ∠A = angle A - ∠B = angle B - ∠C = angle C

According to the angle bisector theorem: - AL bisects ∠A, so (BL/CL) = (AB/AC) - BN bisects ∠B, so (CN/AN) = (BC/AB) - CK bisects ∠C, so (AK/BK) = (AC/BC)

We can use these ratios to find the angles. Let's calculate the angle AOK.

Calculation

Given: - ∠A = 54 degrees - ∠B = 82 degrees

Using the angle bisector theorem, we can find the angles: - (BL/CL) = (AB/AC)- (CN/AN) = (BC/AB)- (AK/BK) = (AC/BC) Let's calculate the angle AOK using the given angles and the angle bisector theorem.