In triangle ABC, angle a = 100 °, angle c = 40 ° a) prove that triangle ABC is isosceles indicate its lateral sides

In triangle ABC, angle a = 100 °, angle c = 40 ° a) prove that triangle ABC is isosceles indicate its lateral sides b) segment ck-bisector of this triangle. Find the angles it makes with side ab

a) The sum of the angles of the triangle is 180: A + B + C = 100 + B + 40 = 140 + B = 180, B = 40.

B = C = 40 (the angles of the triangle at the base are equal), by the property of an isosceles triangle AB = AC – an isosceles triangle.

b) Consider ΔАCK: CАВ = 100, АCК = 20, therefore АCC = 180 – 100 – 20 = 60.

AKB – unfolded angle, AKB = 180.

Also AKB = AKC + CKB, from where:

CKB = AKB – AKC = 180 – 60 = 120.

Answer: AKC = 60, AKB = 120.