Angle B Cc4761

1. **State the problem:** We have a right triangle with legs of length $4$ and a right angle at the bottom-right vertex. We need to find the measure of angle $B$ at the top vertex. 2. **Identify the triangle type:** Since both legs are equal ($4$ and $4$), the triangle is an isosceles right triangle. 3. **Recall the property of isosceles right triangles:** The two angles opposite the equal legs are equal. 4. **Use the angle sum property of triangles:** The sum of angles in any triangle is $180^\circ$. Since one angle is $90^\circ$, the other two angles must sum to $90^\circ$. 5. **Calculate angle $B$:** Since the two angles are equal, each is $\frac{90^\circ}{2} = 45^\circ$. **Final answer:** $$\boxed{45^\circ}$$