Line AB and CD are parallel and P is any point between them. Show that angleABP + angleCDP = angleDPB
Given AB || CD.
Let EF be the parallel line to AB and CD which passes through P.
It can be seem from the figure
∠ABP = ∠BPF (Alternate int. angles)
∠CDP = ∠DPF (Alternate int. angles)
⇒ ∠ABP + ∠CDP = ∠BPF + ∠DPF
⇒ ∠ABP + ∠CDP = ∠DPB
Hence proved!!