The diagonals AC and BD of a rectangle ABCD intersect each other at P. If ABD =50°, then DPC =

Given that,

ABD = ABP = 50°


PBC +ABP = 90° (Each angle of a rectangle is a right angle)


PBC = 40°


Now,


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


Therefore,


BCP = 40° (Equal sides has equal angle)


In triangle BPC,


BPC + PBC + BCP = 180° (Angle sum property of a triangle)


BPC = 100°


BPC + DPC = 180° (Angles in a straight line)


DPC = 180o – 100o


= 80°

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