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 = 50^{0}

Angle PBC + Angle ABP = 90^{0} (Each angle of a rectangle is a right angle)

Angle PBC = 40^{0}

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

Therefore,

Angle BCP = 40^{0} (Equal sides has equal angles)

In triangle BPC,

Angle BPC + Angle PBC + Angle BCP = 180^{0} (Angle sum property of a triangle)

Angle BPC = 100^{0}

Angle BPC + Angle DPC = 180^{0} (Angles in a straight line)

Angle DPC = 180^{0} - 100^{0} = 80^{0}.

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