Angle bisectors AX and BY of triangle ABC meet at point I. Find angle C in degrees, if angle AIB= degrees.
+137 angle C = 38 degrees
Step-by-step explanation:
Refer to attached figure (sorry, forgot to attach earlier)
Given
AIB = 109
Let
CAX = XAB = x
CBY = YBA = y
XIB = YIA = x+y ........exterior angles
XIB = YIA = 180-109 = 71 ............ sum of angles on a line
=>
x+y = 71
ACB = 180 - 2x -2y ................. sum of angles of a triangle
= 180 - 2(x+y)
= 180 - 2(71)
= 180 - 142
= 38
