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# geometry, part two

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74
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+30

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
+2448
+1

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