Question

(a) name the vertex of ∠1. (b) name the sides of ∠tqr. (c) write two other names for ∠2.

Explanation:

Step1: Recall vertex - angle relationship

The vertex of an angle is the common endpoint of the rays that form the angle. For ∠1, the common endpoint of the rays is Q.

Step2: Recall sides - angle relationship

The sides of an angle are the rays that form the angle. For ∠TQR, the rays are $\overrightarrow{QT}$ and $\overrightarrow{QR}$.

Step3: Recall angle - naming conventions

An angle can be named by the vertex (when there is no ambiguity), or by three points with the vertex in the middle. For ∠2, other names are ∠RQS and ∠SQR.

Answer:

(a) Q
(b) $\overrightarrow{QT}$, $\overrightarrow{QR}$
(c) ∠RQS, ∠SQR