Question

The diagonals AC and BD of a rectangle intersect at P , If ∠ABD = 55 degrees,then find ∠DPA

Answer 1

Answer:

Step-by-step explanation:

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 BPC = 1800 - 1000  = 800 degree

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