Question

use the figure to complete each part.
(a) name the sides of ∠tqr.
and
(b) write two other names for ∠2.
and
(c) name the vertex of ∠1.

Explanation:

Part (a)

Step 1: Recall angle side definition

An angle's sides are the two rays forming it. For \( \angle TQR \), the vertex is \( Q \), so the sides are rays \( QT \) and \( QR \).

Step 2: Identify the rays

From the figure, \( \angle TQR \) is formed by \( \overrightarrow{QT} \) and \( \overrightarrow{QR} \).

Part (b)

Step 1: Recall angle naming rules

An angle can be named by vertex and two points (one on each side), with vertex in the middle, or by vertex if unique. For \( \angle 2 \) (at \( Q \), between \( QR \) and \( QS \)), names are \( \angle RQS \) and \( \angle SQR \).

Part (c)

Step 1: Recall vertex definition

The vertex of an angle is the common endpoint of its two sides. For \( \angle 1 \), the sides meet at \( Q \), so vertex is \( Q \).

Answer:

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