the diagonals AC and BD of a rectangle ABCD intersect each other at P. if angle ABD = 50 degree, then angle DPC =

Given: Angle ABD = Angle ABP = 50⁰

Angle PBC + Angle ABP = 90⁰  (Each angle of a rectangle is a right angle)

Angle PBC = 40⁰

Now, PB = PC  (Diagonals of a rectangle are equal and bisect each other)

Therefore,

Angle BCP = 40⁰  (Equal sides has equal angles)

In triangle BPC,

Angle BPC + Angle PBC + Angle BCP = 180⁰  (Angle sum property of a triangle)

Angle BPC = 100⁰

Angle BPC + Angle DPC = 180⁰  (Angles in a straight line)

Angle DPC = 180⁰ - 100⁰ = 80⁰.