jmc

Because angle $QBP$ measures 14 degrees, we know that angle $ABC$ measures $3\cdot 14=42$ degrees. Hence, angle $ACB$ measures $180-39-42=99$ degrees. Next we find that angle $BCP$ measures $\frac{99}{3}=33$ degrees, and finally angle $BPC$ measures $180-14-33=\boxed{133}$ degrees.