Question

list two other ways to name the angle. ∠z choose the correct answer below.
o a. ∠bhp and ∠hbp
o b. ∠pbh and ∠phb
o c. ∠bph and ∠hpb

Explanation:

To name an angle, the middle letter must be the vertex. For $\angle z$ (with vertex \( P \), and sides \( PB \) and \( PH \)), the angle can be named by putting the vertex in the middle. So possible names are \( \angle BPH \) (with \( B \)-vertex-\( P \)-vertex-\( H \)) and \( \angle HPB \) (with \( H \)-vertex-\( P \)-vertex-\( B \)). Checking the options:

• Option A: \( \angle BHP \) has vertex \( H \), \( \angle HBP \) has vertex \( B \) – incorrect.
• Option B: \( \angle PBH \) has vertex \( B \), \( \angle PHB \) has vertex \( H \) – incorrect.
• Option C: \( \angle BPH \) and \( \angle HPB \) both have vertex \( P \) – correct.

Answer:

C. \( \angle BPH \) and \( \angle HPB \)