+5 Angle bisectors $\overline{AX}$ and $\overline{BY}$ of triangle $ABC$ meet at point $I$. Find $\angle C,$ in degrees, if $\angle AIB = 109^\circ$. Could you please help. I just need a few hints. I don't want the answer.
+23246 To make the calculations easier, let angle(B) = 2b and angle(A) = 2a.
To make the description easier, let point X be on BC and point Y be on AC.
In triangle(AXB), write angle(AXB) in terms of a and b. Then, write angle(CXI) in terms of a and b.
In triangle(AYB), write angle(AYB) in terms of a and b. Then, write angle(CYI) in terms of a and b.
Looking at triangle(AIB), how many degrees are in a + b?
How many degrees are in angle(XIY)?
Finally, look at quadrilateral(CXIY) --- you can get the answer!
