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Angle bisectors AX and BY of triangle ABC meet at a point I. Find angle C in degrees, if angle AIB is 106 degrees. (Diagram: https://ibb.co/JK7Mzxp)

 Sep 25, 2022
 #1
avatar+2448 
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Let \(\angle IAB = x\) and \(\angle IBA = y\)

 

We know that \(x + y + 106 = 180\), meaning \(x + y = 74\)

 

We also know that \(\angle C = 180 - 2x - 2y = 180 - 2(x+y)\)

 

So, \(\angle C = 180 - 2 \times 74 = \color{brown}\boxed{32}\)

 Sep 25, 2022

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