Question

The diagonals AC and ND of a rectangle ABCD intersect each other at P. If angle ABD=50,find angle DPC​

Answer 1

Given: Angle ABD = Angle ABP = 50°

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

Angle PBC = 40°

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

Therefore,

Angle BCP = 40°(Equal sides has equal angles)

In triangle BPC,

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

Angle BPC = 100°

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

Angle DPC = 180° - 100° = 80°

 

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So angle DPC =100°

Hope it helps