In triangle ABC, AB = BC, BD is the bisector. Find 1) the angle BCA if the adjacent angle at the vertex A

In triangle ABC, AB = BC, BD is the bisector. Find 1) the angle BCA if the adjacent angle at the vertex A is 130 degrees. 2) Perimeter of triangle ABC, if AB = 5cm, AD = 2cm

1)

The outer angle KAB is adjacent to the angle BAC, the sum of which is 180, then the angle BAC = 180 – 130 = 50.

Since, by condition, AB = BC, the triangle ABC is isosceles, and then the angles at the base of the AC are equal. Angle ACB = BAC = 50.

The sum of the inner angles of the triangle is 100, then the angle ABC = 180 – 50 – 50 = 80.

Answer: Angle ABC is 80.

2)

Since the triangle is isosceles, then the bisector BD, in the triangle, is also the median of the triangle, then CD = AD = 2 cm, then AC = AD + CD = 2 + 2 = 4 cm.

Determine the perimeter of the triangle. P = AB + BC + AC = 5 + 5 + 4 = 14 cm.

Answer: The perimeter of the triangle is 14 cm.