In triangle DEF, angle D = 76 °, F = 60 °. Find the angle between the bisectors of angle D and angle E.

Using the property of the angles of the triangle (their sum is 180 °), we find the value of the angle E:
E = 180 – 76 – 60 = 44 °.
Denoting the intersection point of the bisectors by M, consider the triangle DME:
D = 76: 2 = 38 °;
E = 44: 2 = 22 °.
Then, relying on the above property:
M = 180 – 38 – 22 = 120 °.
Answer: the bisectors form an angle of 120 ° with each other.