Angle bisectors AX and BY of triangle ABC meet at point I. Find angle C in degrees, if angle AIB= 106 degrees.

Since angle AIB  =  106

Then    angle (A  / 2) +   angle( B /2)  + 106  =180

A/2 + B/2 =  180-106

A/2 + B/2  =  74

A + B =  148

So

C =  180   -  148  =  32°