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

In a triangle ABC AB = 4cm, BC = 7cm, AC = 6cm, and in a triangle MNK MK = 8cm, MN = 12cm, KN = 14cm. Find the angles of the triangle MNK if A = 80⁰, B = 60⁰.

Given:
triangles ABC and MNK,
AB = 4cm,
BC = 7cm,
AC = 6cm,
MN = 12cm,
KN = 14cm,
MK = 8cm,
angle A = 80⁰,
angle B = 60⁰.
Find the degree measures of the angles M, N, K -?
Solution:
1) Consider the triangle ABC.
angle C = 180 – (angle A + angle B);
angle C = 180 – (80 + 60);
angle C = 40⁰;
2) The ABC triangle is similar to the MNK triangle, since
KN / BC = MN / AC = MK / AB;
14/7 = 12/6 = 8/4 = 2.
Therefore, in such triangles the angles are corresponding equal.
Then the angle N = angle C = 40⁰,
angle M = angle A = 80⁰,
angle K = angle B = 60⁰.
Answer: 60⁰, 80⁰, 40⁰.