Find the solution to this math problem.

Find the solution to this math problem.

As shown in the figure, ray AC∨BD. When points P, Q and R fall between two rays, please write an equation between ∠ APQ ∠ PQB ∠ PQR ∠ RBD and prove it.

Tip: parallel BD with AC.

Connect AQ, BQ and CD as shown.

Reduce the concave angle? The outward and outward protruding angles add up to form a closed convex polygon.

Then use that formula of polygon inner angle,

We can get the equivalent relationship among angle APQ, angle PAC, angle PQR, angle QRB and angle RBD.

Solution: There are equivalent relationships among APQ angle, PAC angle, PQR angle, QRB angle and RBD angle:

∠PAC+∠PQR+∠QBD-∠APQ-∠QRB=π.

Proof: connect AQ, BQ, CD

Then ∠PAC+∠PQR+∠QBD-∠APQ-∠QRB.

=∠PAC+∠PQR+∠QBD-[π-(∠PAQ+∠AQP)]-[π-(∠RQB+∠QBR)]

=∠PAC+∠PQR+∠QBD+∠PAQ+∠AQP+∠RQB+∠QBR-π-π

= (sum of internal angles of convex pentagonal CAQBD) -(∠ACD+∠BDC)-π

=3π-π-π=π