The diagonals of a quadrilateral ABCD bisect each other. In this quadrilateral, if ∠A = 45° then ∠B = ?

Correct option is B

Given:

Quadrilateral ABCD with diagonals that bisect each other.

∠A = 45°

Concept Used:

Parallelogram Properties: If the diagonals of a quadrilateral bisect each other, then the quadrilateral is a parallelogram.

Opposite Angles of a Parallelogram: Opposite angles in a parallelogram are equal.

Adjacent Angles of a Parallelogram: Adjacent angles in a parallelogram are supplementary (their sum is 180°).

Solution:

Since the diagonals of quadrilateral ABCD bisect each other, ABCD is a parallelogram.

Because ABCD is a parallelogram, opposite angles are equal. However, we are given ∠A and asked to find ∠B, which are adjacent angles, not opposite.

Adjacent angles in a parallelogram are supplementary.

Therefore, ∠A + ∠B = 180°.

45° + ∠B = 180°

∠B = 180° - 45°

∠B = 135°

Option (B) is right.