Triangle Angle 3Ae04D

1. **State the problem:** We have a right triangle with vertices $A$, $B$, and $C$, where angle $C$ is the right angle ($90^\circ$), and angle $A$ measures $55^\circ$. We need to find the measure of angle $B$. 2. **Recall the triangle angle sum rule:** The sum of the interior angles in any triangle is always $180^\circ$. That is, $$\text{angle } A + \text{angle } B + \text{angle } C = 180^\circ$$ 3. **Apply the known values:** Since angle $C$ is a right angle, $$\text{angle } C = 90^\circ$$ and angle $A = 55^\circ$. 4. **Set up the equation:** $$55^\circ + \text{angle } B + 90^\circ = 180^\circ$$ 5. **Simplify the left side:** $$\cancel{55^\circ} + \text{angle } B + \cancel{90^\circ} = 180^\circ$$ $$145^\circ + \text{angle } B = 180^\circ$$ 6. **Solve for angle $B$:** $$\text{angle } B = 180^\circ - 145^\circ$$ $$\text{angle } B = 35^\circ$$ 7. **Conclusion:** The measure of angle $B$ is $35^\circ$.