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!!

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