In the given figure, two line segments AC and BD intersect each other at the Point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠APB = 50° and ∠CDP = 30° then ∠PBA = ?

Question

In the given figure, two line segments AC and BD intersect each other at the Point P such that PA = 6 cm, PB = 3 cm, PC = 2.5 cm, PD = 5 cm, ∠ APB = 50° and ∠ CDP = 30° then ∠ PBA = ?

Philoid · Accepted Answer

In ΔAPB and Δ DPC,
∠APB = ∠DPC = 50°

By SAS property, Δ APBDPC
∠PBA = ∠DPC
In Δ DPC,
∠D + ∠ P + ∠C = 180°

∠ C = 100°
∴ ∠PBA = ∠DPC = 100°