+0  
 
0
43
1
avatar

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)?

 May 15, 2022
 #1
avatar+9457 
0

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, \(\angle ACP = \angle ACB - \angle PCB = 64^\circ - 52^\circ = 12^\circ\).

 May 15, 2022

10 Online Users