Final answer:
In a quadrilateral where the diagonals bisect each other, such as a parallelogram, opposite angles are equal. Given ∠A=45°, ∠B must be 135° by using the properties of angles in a parallelogram and the sum of internal angles in a quadrilateral.
Step-by-step explanation:
If the diagonals of a quadrilateral ABCD bisect each other, the quadrilateral is a parallelogram. By the properties of a parallelogram, opposite angles are equal. Therefore, if ∠A=45°, then ∠C=45° as well.
Since the sum of angles in a quadrilateral is 360 degrees, we can find ∠B by knowing that the sum of angles ∠A + ∠B + ∠C + ∠D is 360 degrees. Given that ∠B and ∠D are opposite angles, they must be equal.
This gives us the equation: 45° + ∠B + 45° + ∠B = 360°. Thus, 2∠B + 90° = 360°, which simplifies to 2∠B = 270°. Dividing both sides by 2 gives us ∠B = 135°.