In triangle ABC AB = 4 cm, BC = 7 cm, AC = 6 cm, and in triangle MNK Mk = 8 cm, MN = 12 cm KN = 14 cm

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

It is easy to see that AB / MK = AC / KN = BC / MN = 1/2. That is, triangle ABC is similar to triangle MNK with a similarity factor of 1/2. Then the angles of the triangles are equal. Since the sum of the angles of the triangles is 180 °, then:

C = 180 ° – 80 ° – 60 ° = 40 °.

Then:

M = A = 80 °;

N = B = 60 °;

K = C = 40 °.

Answer: the required angles are 80 °, 60 ° and 40 °, respectively.