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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)?

Guest May 15, 2022

MaxWong · Answer 1 · 2022-05-15T08:07:22

This is the diagram.

Note that $\angle BPC = 180^\circ - 116^\circ = 64^\circ$ .

Since BC = CP, $\angle PBC = 64^\circ$ .

Considering the interior angle sum of $\triangle BPC$ gives $\angle PCB = 52^\circ$ .

Since AB = AC, $\angle ACB = \angle ABC = \angle PBC = 64^\circ$ .

Therefore, $\angle ACP = \angle ACB - \angle PCB = 64^\circ - 52^\circ = 12^\circ$ .