It is proved that ≈ 1 is the external angle of △ABP.
∴∠ 1=∠BAP+∠ABP
What's Ad, be and cf? Angle bisector of △ABC
∴∠BAP+∠ABP+∠DCG= 180 /2=90
∴∠ 1+∠DCG=90
∵PG⊥BC in G
∴∠2++∠DCG=90
∴∠ 1=∠2?
Is that clear? Let me know if you have any questions.