Question

ABCD is a parallelogram . P is any point within it . Prove that Angle APD = Angle PAB + Angle PDC​

Answer 1

Given info : ABCD is a parallelogram. P is any point within it.

Prove that ∠APD = ∠PAB + ∠PDC

proof : draw a line XY || AB || CD which is passing through point P as shown in figure.

from the rule of parallel lines,

∠PAB = ∠APX ...(1)

∠PDC = ∠XPD ...(2)

adding equations (1) and (2) we get,

∠PAB + ∠PDC = ∠APX + ∠XPD = ∠APD [ see figure ]

Therefore ∠APD = ∠PAB + ∠PDC.

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