In ΔABC and ΔRQP,
ABRQ=3.87.6=12
BCQP=612=12
and CAPR=3√36√3=12
⇒ABRQ=BCQP=CAPR (1 mark)
So, ΔABC∼ΔRQP (By SSS similarity criterion)
∴∠C=∠P(Corresponding angles of similar triangles are equal) (1 mark)
But, ∠C=180∘−∠A−∠B(By angle sum property)
∠C=180∘−80∘−60∘=40∘
So, ∠P=40∘ (1 mark)