Question

Diagonals of a quadrilateral ABCD bisect each other. If ∠A = 45°, determine ∠B.

Answer 1

35 is the answer to this question

Answer 2

∠B =  135°

Explanation:

Given: Diagonals of a quadrilateral ABCD bisect each other. ∠A = 45°.

To find: ∠B.

Properties of a parallelogram are:

1. Both pairs of opposite sides are parallel.
2. Both pairs of opposite sides are congruent.
3. Both pairs of opposite angles are congruent.
4. Consecutive angles are supplementary.
5. Diagonals bisect each other.

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

In the parallellogram ABCD, we know that adjacent angles are supplementary.

So ∠A + ∠B =  180°

45° + ∠B =  180°

∠B =  180° - 45°  

∠B =  135°

Thus solved.