In triangle ABC, side AB = 4 cm, BC = 7 cm, AC = 6 cm, and in triangle MNK = 8 cm

In triangle ABC, side AB = 4 cm, BC = 7 cm, AC = 6 cm, and in triangle MNK = 8 cm, MN = 12 cm, KN = 14 cm.Find the angles of triangle MNK if angle A = 80 °, angle B = 60 °

1) Consider the triangle ABC

angle A = 80 °;

angle B = 60 °;

angle C – unknown, find angle C.

angle C = 180 ° – angle A – angle B;

angle С = 180 ° – 80 ° – 60 °;

angle C = 40 °.

2) triangle ABC is similar to triangle MNK,

since AB / MK = BC / NK = CA / NM;

4/8 = 7/14 = 6/12 = ½;

Therefore, the angles in triangle ABC and in triangle MNK are equal.

Then the angle N = angle C = 40 °;

angle N = 40 °.

angle M = angle A = 80 °;

angle M = 80 °.

angle K = angle B = 60 °;

angle K = 60 °.

Answer: The MNK triangle has angles: 80 °, 60 °, 40 °.