In Fig, lines AB and CD are parallel and P is any point as shown in th

1.	In Fig, lines AB and CD are parallel and P is any point as shown in the figure. Show that ∠ABP +∠CDP = ∠DPB.
Answer» Given that, AB ‖ CD Let, EF be the parallel line to AB and CD which passes through P. It can be seen from the figure that alternate angles are equal ∠ABP = ∠BPF ∠CDP = ∠DPF ∠ABP + ∠CDP = ∠BPF + ∠DPF ∠ABP + ∠CDP = ∠DPB Hence, proved

In Fig, lines AB and CD are parallel and P is any point as shown in the figure. Show that ∠ABP +∠CDP = ∠DPB.

Answer»

Given that,

AB ‖ CD

Let, EF be the parallel line to AB and CD which passes through P.

It can be seen from the figure that alternate angles are equal

∠ABP = ∠BPF

∠CDP = ∠DPF

∠ABP + ∠CDP = ∠BPF + ∠DPF

∠ABP + ∠CDP = ∠DPB

Hence, proved