Question

Помогите решить даю 10 баллов! В треугольнике ABC угол В=50градусов,угол С=70 градусов.Биссектрисы AK и BM треугольника ABC пересекаются в точку О.Найдите угол KOM. Решите пожалуйста подробно!)

Answer 1

Решение на листочке

Ответ: 125°

Answer 2

Given Information

We are given that in triangle ABC, angle B is 50 degrees and angle C is 70 degrees. The bisectors AK and BM of triangle ABC intersect at point O. We need to find the angle KOM.

Solution

To find the angle KOM, we can use the angle bisector theorem and angle sum property of triangles.

Let's start by finding the measures of angles A, B, and C using the angle sum property of triangles. The sum of the angles in a triangle is always 180 degrees.

Angle A = 180 - (angle B + angle C) Angle A = 180 - (50 + 70) Angle A = 180 - 120 Angle A = 60 degrees

Now, let's consider triangle ABC. Since AK is the angle bisector of angle A, it divides angle A into two equal angles. Similarly, BM is the angle bisector of angle B, so it divides angle B into two equal angles.

Let's denote the point of intersection of AK and BM as point O. Since AK is the angle bisector of angle A, we can say that angle OAK = angle OAB. Similarly, angle OBM = angle OBA.

Now, let's consider triangle AOB. The sum of the angles in a triangle is always 180 degrees. Therefore, we can write:

angle OAB + angle OBA + angle BOA = 180 degrees

Since angle OAK = angle OAB and angle OBM = angle OBA, we can substitute these values:

angle OAK + angle OBM + angle BOA = 180 degrees

Since angle OAK and angle OBM are equal, let's denote them as angle x:

2x + angle BOA = 180 degrees

Now, let's consider triangle BOC. The sum of the angles in a triangle is always 180 degrees. Therefore, we can write:

angle BOC + angle OBC + angle OCB = 180 degrees

Since angle OBM = angle OBA and angle OBC = angle OCB, we can substitute these values:

angle BOC + angle OBM + angle OBC = 180 degrees

Since angle OBM and angle OBC are equal, let's denote them as angle y:

angle BOC + 2y = 180 degrees

Now, let's consider triangle BOK. The sum of the angles in a triangle is always 180 degrees. Therefore, we can write:

angle BOK + angle BOA + angle KOB = 180 degrees

Since angle BOA is equal to angle OAK + angle OAB, we can substitute these values:

angle BOK + (2x + angle OAB) + angle KOB = 180 degrees

Since angle OAB is equal to angle OBM, we can substitute this value:

angle BOK + (2x + angle OBM) + angle KOB = 180 degrees

Since angle OBM is equal to angle OBC, we can substitute this value:

angle BOK + (2x + angle OBC) + angle KOB = 180 degrees

Since angle OBC is equal to angle OCB, we can substitute this value:

angle BOK + (2x + angle OCB) + angle KOB = 180 degrees

Since angle OCB is equal to angle OCM + angle MCB, we can substitute these values:

angle BOK + (2x + angle OCM + angle MCB) + angle KOB = 180 degrees

Since angle OCM is equal to angle OBM, we can substitute this value:

angle BOK + (2x + angle OBM + angle MCB) + angle KOB = 180 degrees

Since angle OBM is equal to angle OBA, we can substitute this value:

angle BOK + (2x + angle OBA + angle MCB) + angle KOB = 180 degrees

Since angle OBA is equal to angle OAK + angle OAB, we can substitute these values:

angle BOK + (2x + angle OAK + angle OAB + angle MCB) + angle KOB = 180 degrees

Since angle OAK is equal to angle OAB, we can substitute this value:

angle BOK + (2x + angle OAB + angle OAB + angle MCB) + angle KOB = 180 degrees

Simplifying the equation:

angle BOK + (4x + angle MCB) + angle KOB = 180 degrees

Since angle MCB is equal to angle KCB, we can substitute this value:

angle BOK + (4x + angle KCB) + angle KOB = 180 degrees

Since angle KCB is equal to angle KCM + angle MCB, we can substitute these values:

angle BOK + (4x + angle KCM + angle MCB) + angle KOB = 180 degrees

Since angle MCB is equal to angle MBC, we can substitute this value:

angle BOK + (4x + angle KCM + angle MBC) + angle KOB = 180 degrees

Since angle MBC is equal to angle MBO + angle OBC, we can substitute these values:

angle BOK + (4x + angle KCM + angle MBO + angle OBC) + angle KOB = 180 degrees

Since angle MBO is equal to angle MBO + angle OBM, we can substitute these values:

angle BOK + (4x + angle KCM + angle MBO + angle OBM + angle OBC) + angle KOB = 180 degrees

Since angle OBM is equal to angle OBA, we can substitute this value:

angle BOK + (4x + angle KCM + angle MBO + angle OBA + angle OBC) + angle KOB = 180 degrees

Since angle OBA is equal to angle OAK + angle OAB, we can substitute these values:

angle BOK + (4x + angle KCM + angle MBO + angle OAK + angle OAB + angle OBC) + angle KOB = 180 degrees

Since angle OAK is equal to angle OAB, we can substitute this value:

angle BOK + (4x + angle KCM + angle MBO + angle OAB + angle OAB + angle OBC) + angle KOB = 180 degrees

Simplifying the equation:

angle BOK + (4x + angle KCM + angle MBO + 2 * angle OAB + angle OBC) + angle KOB = 180 degrees

Since angle OAB is equal to angle OBM, we can substitute this value:

angle BOK + (4x + angle KCM + angle MBO + 2 * angle OBM + angle OBC) + angle KOB = 180 degrees

Since angle OBM is equal to angle OBA, we can substitute this value:

angle BOK + (4x + angle KCM + angle MBO + 2 * angle OBA + angle OBC) + angle KOB = 180 degrees

Since angle OBA is equal to angle OAK + angle OAB, we can substitute these values:

angle BOK + (4x + angle KCM + angle MBO + 2 * (angle OAK + angle OAB) + angle OBC) + angle KOB = 180 degrees

Since angle OAK is equal to angle OAB, we can substitute this value:

angle BOK + (4x + angle KCM + angle MBO + 2 * (angle OAB + angle OAB) + angle OBC) + angle KOB = 180 degrees

Simplifying the equation:

angle BOK + (4x + angle KCM + angle MBO + 4 * angle OAB + angle OBC) + angle KOB = 180 degrees

Since angle KCM is equal to angle KCB, we can substitute this value:

angle BOK + (4x + angle KCB + angle MBO + 4 * angle OAB + angle OBC) + angle KOB = 180 degrees

Since angle KCB is equal to angle KCM + angle MCB, we can substitute these values:

angle BOK + (4x + angle KCM + angle MCB + angle MBO + 4 * angle OAB + angle OBC) + angle KOB = 180 degrees

Since angle MCB is equal to angle MBC, we can substitute this value:

angle BOK + (4x + angle KCM + angle MBC + angle MBO + 4 * angle OAB + angle OBC) + angle KOB = 180 degrees

Since angle MBC is equal to angle MBO + angle OBC, we can substitute these values:

angle BOK + (4x + angle KCM + angle MBO + angle OBC + angle MBO + 4 * angle OAB + angle OBC) + angle KOB = 180 degrees

Since angle MBO is equal to angle MBO + angle OBM, we can substitute these values:

angle BOK + (4x + angle KCM + angle MBO + angle OBC + angle MBO + angle OBM + 4 * angle OAB + angle OBC) + angle KOB = 180 degrees

Since angle OBM is equal to angle OBA, we can substitute this value:

angle BOK + (4x + angle KCM + angle MBO + angle OBC + angle MBO + angle OBA + 4 * angle OAB + angle OBC) + angle KOB = 180 degrees

Since angle OBA is equal to angle OAK + angle OAB, we can substitute these values:

angle BOK + (4x + angle KCM + angle MBO + angle OBC +