1. **Problem Statement:** Given a figure with point Q and rays QS, QR, and QT, and two angles labeled 1 and 2 at vertex Q, we need to name the sides and vertices of the angles as requested. 2. **Part (a): Name the sides of \(\angle T Q R\).** - The sides of an angle are the two rays that form the angle. - \(\angle T Q R\) is the angle at vertex Q formed by rays QT and QR. - Therefore, the sides are \(\overrightarrow{Q T}\) and \(\overrightarrow{Q R}\). 3. **Part (b): Write two other names for \(\angle 2\).** - \(\angle 2\) is the angle at vertex Q between rays QS and QR. - Angles can be named by their vertex and one point on each side. - So, two other names for \(\angle 2\) are \(\angle S Q R\) and \(\angle R Q S\). 4. **Part (c): Name the vertex of \(\angle 1\).** - \(\angle 1\) is the angle at point Q between rays QR and QT. - The vertex of \(\angle 1\) is \(Q\). **Final answers:** - (a) Sides of \(\angle T Q R\): \(\overrightarrow{Q T}\) and \(\overrightarrow{Q R}\) - (b) Other names for \(\angle 2\): \(\angle S Q R\) and \(\angle R Q S\) - (c) Vertex of \(\angle 1\): \(Q\)