Question

naming angles, sides of angles, and vertices
(a) name the sides of \\( \angle t q r \\).
and
(b) write two other names for \\( \angle 2 \\).
and
(c) name the vertex of \\( \angle 1 \\).

Explanation:

Step1: Recall the definition of an angle's sides

An angle is formed by two rays with a common endpoint. For \(\angle TQR\), the rays (sides) are \(\overrightarrow{QT}\) and \(\overrightarrow{QR}\).

Step2: Rename \(\angle2\)

An angle can be named by its vertex (if there is no ambiguity) or by three - letter notation. Since \(\angle2\) has vertex \(Q\), two other names are \(\angle RQS\) (using three - letter notation with the vertex in the middle) and \(\angle SQR\) (another valid three - letter combination as the order of non - vertex letters can be interchanged when the vertex is clear).

Step3: Identify the vertex of \(\angle1\)

The vertex of an angle is the common endpoint of its sides. For \(\angle1\), the vertex is \(Q\).

Answer:

(a) \(\overrightarrow{QT}\) and \(\overrightarrow{QR}\)
(b) \(\angle RQS\) and \(\angle SQR\)
(c) \(Q\)