Question

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

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Answer 1

Answer:

The diagonals AC and BD of rectangle ABCD intersect at P. Also, diagonals of rectangle are equal and they bisect each other. But ∠APB and ∠DPC are vertically opposite angles.

Answer 2

Given, ABCD is a rectangle

We know that the diagonals of rectangle are same and bisect each other

So, we have

AP = BP

∠PAB = ∠PBA (Equal sides have equal opposite angles)

∠PAB = 50o (Since, given ∠PBA = 50o)

Now, in ∆APB

∠APB + ∠ABP + ∠BAP = 180o

∠APB + 50o + 50o = 180o

∠APB = 180o – 100o

∠APB = 80o

Then,

∠DPB = ∠APB (Vertically opposite angles)

Hence,

∠DPB = 80o