1. **Problem Statement:** We are given an isosceles right triangle with a right angle at the top vertex and two equal sides indicated. We need to find the size of the angle marked $x$ at the bottom-left corner. 2. **Key Properties:** In an isosceles right triangle, the two legs are equal in length, and the angle opposite each leg is equal. The right angle measures $90^\circ$. 3. **Formula and Reasoning:** The sum of angles in any triangle is $180^\circ$. Since one angle is $90^\circ$ (right angle), the other two angles must sum to $90^\circ$. 4. **Calculation:** Because the triangle is isosceles, the two non-right angles are equal. Let each be $x$. $$x + x + 90^\circ = 180^\circ$$ $$2x = 180^\circ - 90^\circ$$ $$2x = 90^\circ$$ $$x = \frac{90^\circ}{2} = 45^\circ$$ 5. **Conclusion:** The size of the angle marked $x$ is $45^\circ$.