On the continuation of side AB of triangle ABC beyond point A, point K is taken so that AK = AC

| September 17, 2021 | education

On the continuation of side AB of triangle ABC beyond point A, point K is taken so that AK = AC, and on its continuation beyond point B, point M is taken so that BM = BC. Find the angles of the triplet MKC if the angle BAC = 70, ABC = 80 degrees.

In triangle ABC, angle BAC is 70 °, angle ABC is 80 °. Find the angle of the BCA (the sum of the angles in the triangle is 180 °):

180 ° – (70 ° + 80 °) = 30 °.

Let AC = x, then KC will be equal to 2x (AK = AC). Let BC = y, then MC will be equal to 2y (BM = BC).

Consider triangles ABC and ISS: angle C is common; AC / KC = x / 2x = 1/2; BC / MC = y / 2y = 1/2.

Consequently, triangles are similar in two sides and the angle between them.

For similar triangles, the corresponding angles are equal.

Hence, the angle K is equal to the angle A = 70 °, the angle M is equal to the angle B = 80 °, the angle C is equal to 30 °.



One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.