Question

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

Answer 1

Answer:

∠DPB=80

Step-by-step explanation:

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=50

o

 (Since, given ∠PBA=50

o

Now, in △APB

∠APB+∠ABP+∠BAP=180

o

∠APB+50

o

+50

o

=180

o

∠APB=180

o

−100

o

∠APB=80

o

Then,

∠DPB=∠APB (Vertically opposite angles)

Hence,