The sides AB and AC of ΔABC are produced up to points D and E. The bisectors of the exterior angles so formed, intersect each other at point I. If ∠ACB is 66° and ∠ABC = 44°, then what is the measure (in degrees) of ∠BIC ?

55

We know that,

The sum of the angles of the triangle = 180^o

∠A = 180° - (44° + 66°)

= ∠A = 70° 

∠BIC = 90 - ∠A/2 (Exterior angle bisector)

∠BIC = 90 - 70/2

= 90 - 35 = 55°