In triangle ABC, AB = AC. Point P lies on line AB such that CP = BC. If angle APC = 116 degrees, what is angle ACP(in degrees)?
Angle ACP = 12 degrees
A
P 116
B C
Since APC = 116
Then BPC = 180 - 116 = 64
And CP = BC
So angle PBC = angle BPC = 64
And since AB = AC
Then angle ABC = angle PBC = angle ACB = 64
And angle PCB = 180 - 2 (64) = 180 - 128 = 52
So
ACP = ACB - PCB = 64 - 52 = 12°
