Question

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

Answer 1

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.

 

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Answer 2

Answer:

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