Question 118
Let $ABCD$ be a convex quadrilateral. Let $I_A, I_B, I_C$, and $I_D$ be the incenters of the triangles $DAB$, $ABC$, $BCD$, and $CDA$, respectively. Given that $\angle B I_A A + \angle I_C I_A I_D = 180^\circ$, prove that $\angle B I_B A + \angle I_C I_B I_D = 180^\circ$.