Find the largest angle of Triangle ABC in the following image?

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From angle calculations in a triangle to be 180 degrees, it is clear that the sum of angles PBC and PCB is 80 degrees.

Now,

comparison of angles in triangle APB shows that the length of PB is larger than AP.

comparison of angles in triangle APC shows that the length of AP is larger than AC

therefor the length of PB is larger than PC resulting the angle PCB is larger than PBC, even if these two angles were equal, would result to angle C to be the largest angle.

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