Question

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

(a) 70°

(b) 90°

(c) 80°

(d) 100°

Answer 1

Figure can be drawn as follows:

The diagonals AC and BD of rectangle ABCD intersect at P.

Also, it is given that

We need to find

It is given that

Therefore, (Because P lies on BD)

Also, diagonals of rectangle are equal and they bisect each other.

Therefore,

Thus, (Angles opposite to equal sides are equal)

[(Given)]

By angle sum property of a triangle:

But and are vertically opposite angles.

Therefore, we get:

[(Already proved)]

Hence the correct choice is (c).