What angles are formed when two bisectors of an equilateral triangle intersect?

Each of the corners of an equilateral triangle is 60 °.

Consider a triangle formed by two bisectors and the third side of an equilateral triangle.

In it, the degree measures of the angles between the bisectors and the third side of an equilateral triangle are equal to half the degree measures of the angles of an equilateral triangle, that is, their degree measures
60 ° / 2 = 30 °.

Since the sum of the angles of any triangle is 180 °, the angle formed by the intersection of two bisectors of an equilateral triangle will be 180 ° – 30 ° – 30 ° = 120 °.

The adjacent angle to this angle is 180 ° – 120 ° = 60 °.

So, the bisectors of an equilateral triangle at intersection form angles of 120 ° and 60 °.

Answer: 120 ° and 60 °.