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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)?

 Jan 17, 2022
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First we know that ABC is an isosceles triangle. On line AB, there is a point P that makes CPB an isosceles triangle as well. Angle APC is 116. That means angle CPB is 180-116=64 degrees. Since triangle CPB is isosceles, angle PBC is also 64 degrees. That makes angle PCB 180-(64+64)=180-128=52 degrees. As you may recall, triangle ABC is isosceles, so angle ACP+52=64. Solving for the angle, we get ACP=64-52=12 degrees. (By the way, sorry there's no picture to show you my thinking.)

 Jan 18, 2022
edited by PikachuLovesKetchup  Jan 18, 2022

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