In triangle ABC, find the angle between the height BH and the bisector BM if the angle A is 67

In triangle ABC, find the angle between the height BH and the bisector BM if the angle A is 67 degrees and the angle C is 35 degrees

1. Point M is located on the AC side between point H and the vertex C of the triangle ABC.

2. Based on the fact that the total value of all the angles of the triangle is 180 °, we calculate the value of the angle B:

Angle B = 180 ° – 64 ° – 35 ° = 78 °.

3. The bisector BM divides the angle B into two equal parts, that is, the angle CBM = 78 °: 2 = 39 °.

4. Angle СBН = 180 ° – 90 ° – 35 ° = 45 °.

5. Angle MBН between the bisector BM and the height BH = angle СBН – angle СBМ = 45 ° – 39 ° = 6 °.

Answer: the angle МBН between the bisector BM and the height ВН is 6 °.