Question

Angle bisectors AX and of triangle ABC meet at point I. Find angle C in degrees, if AIB = 109.

Answer 1

angle C = 38 degrees

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