1. **Problem Statement:** We have a point B with rays BA, BC, and BD. Angles are labeled 1 and 2. We need to: (a) Name the vertex of \(\angle DBC\). (b) Name the sides of \(\angle 2\). (c) Write two other names for \(\angle 1\). 2. **Understanding Angles:** - The vertex of an angle is the common endpoint where two rays meet. - The sides of an angle are the two rays forming the angle. - An angle can be named by its vertex and points on each side, or by its number label. 3. **Solution:** (a) \(\angle DBC\) means the angle with vertex at point B and sides along points D and C. - The vertex is the middle letter, so the vertex is **B**. (b) \(\angle 2\) is formed by rays BC and BD. - Therefore, the sides of \(\angle 2\) are **ray BC** and **ray BD**. (c) \(\angle 1\) is formed by rays BA and BC. - Two other names for \(\angle 1\) are \(\angle ABC\) and \(\angle CBA\) (vertex B with points A and C on sides). **Final answers:** (a) Vertex of \(\angle DBC\) is **B**. (b) Sides of \(\angle 2\) are **ray BC** and **ray BD**. (c) Two other names for \(\angle 1\) are \(\angle ABC\) and \(\angle CBA\).