In the given problem, triangle B is an enlargement of triangle A, and we need to find the size of angle $x$ in triangle B.

Analysis:

1. Triangle A is a right-angled triangle where both legs are of equal length, 4 cm. This means it is an isosceles right triangle, where the two non-right angles are equal.

   For any isosceles right-angled triangle, the two angles opposite the equal sides are each $45^\circ$, since: $\text{Sum of angles in a triangle} = 180^\circ.$ In a right triangle: $90^\circ (\text{right angle}) + 2 \times \theta = 180^\circ \implies \theta = 45^\circ.$

2. Triangle B is an enlargement of triangle A. Since it is an enlargement, the triangles are similar, meaning all corresponding angles are equal. Therefore, the angle $x$ in triangle B is equal to the corresponding angle in triangle A.

Conclusion:

The size of angle $x$ is: $x = 45^\circ.$

Would you like more details or have any questions?

Here are 5 related questions to expand your understanding:

1. What is the definition of similar triangles and how do their angles and sides relate?
2. How does an enlargement affect the angles and side lengths of a triangle?
3. What is the Pythagorean Theorem, and how could it apply to this problem?
4. Can you find the hypotenuse of triangle A, given its side lengths?
5. How could you use trigonometric ratios to confirm the angle values in this type of triangle?

Tip: For isosceles right triangles, always remember that their angles are $45^\circ, 45^\circ,$ and $90^\circ$.