in the diagram point am is the center of the circle what is m< PON ?

Remember that the angle of an arc substended at the center is twice the angle substended at the circumference.
Using this, we can say that:
[tex]2(\angle PON)=\angle PMN[/tex]Solving for angle PON,
[tex]\begin{gathered} 2(\angle PON)=\angle PMN \\ \rightarrow\angle PON=\frac{\angle PMN}{2} \\ \rightarrow\angle PON=\frac{134}{2} \\ \\ \Rightarrow\angle PON=67 \end{gathered}[/tex]This way, we can conclude that the correct answer is:
B. 67°