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

 Apr 30, 2023
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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

 May 1, 2023

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