In the angle DEF, angle D = 76`, angle F = 60, find the angle between the bisectors of angle D and E.

The sum of the three angles of a triangle is 180 degrees:

D + E + F = 180,

angle E = 180 – (D + F) = 180 – (76 + 60) = 44 degrees.

To determine the angle between the bisectors of angles D and E, it is necessary to consider the triangle formed by the side DE and these bisectors.

Let the point of intersection of the bisectors be A, then the angles in the triangle DEА:

DEA = 0.5 angle E = 0.5 * 44 = 22;

ADE = 0.5 angle D = 0.5 * 76 = 38;

DАE = 180 – (DEА + АDE) = 180 – (22 + 38) = 120.

The angle between the bisectors of angles D and E is 120 degrees.