Question

the diagonals ac and bd of a rectangle abcd intersect each other at p. if angle abd=50 degree,find angle dpc

Answer 1

it would rather be about 130 

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