Question

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

Answer 1

sum of the angles of a triangle is 180
so, from triangle ACP angle of APC will be 180-40-30=110
and from triangle APB angle of APB will be 180-10-20=150
so, angle of CPB = 360-110-150=100
assume angles of PBC and PCB are equal
so,angle A=50
angle B=60
angle C=70 is the largest angle of the triangle

Answer 2

C is the largest angle

Answer 3

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.