By referring given figure,
The value of $$x$$ is calculated as,
$$3x + 15^\circ = 4x - 5^\circ$$ (By vertically opposite angles)
$$3x - 4x = -5^\circ - 15^\circ$$
$$-x = -20^\circ$$
$$x = 20^\circ$$
The value of $$\angle BPD$$ is calculated as,
The sum of adjacent angles is $$180^∘$$
$$\angle BPD+ \angle BPC = 180^\circ $$
$$\angle BPD = 180^\circ - \angle BPC$$
$$= 180^\circ - (4x - 5^\circ)$$
$$= 180^\circ - (4 \times 20^\circ - 5^\circ )$$
$$= 180^\circ - 80^\circ + 5^\circ$$
$$= 105^\circ$$