Question

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

Explanation:

Part (a)

Step1: Identify angle ∠TQR

The angle ∠TQR has vertex at \( Q \), and the two sides are the rays forming the angle. The rays are \( QT \) and \( QR \).

Step2: Confirm the sides

So the sides of \( \angle TQR \) are \( QT \) and \( QR \).

Step1: Recall angle naming

An angle can be named by its vertex and two points on the rays, or by a number. \( \angle 2 \) has vertex \( Q \), and rays \( QS \) and \( QR \). So other names can be \( \angle SQR \) and \( \angle RQS \).

Step2: List the names

Two other names for \( \angle 2 \) are \( \angle SQR \) and \( \angle RQS \).

Step1: Identify vertex of \( \angle 1 \)

The angle \( \angle 1 \) is formed by rays \( QT \) and \( QR \) (or the relevant rays). The vertex of an angle is the common endpoint of the two rays forming the angle. For \( \angle 1 \), the common endpoint is \( Q \).

Step2: Confirm the vertex

So the vertex of \( \angle 1 \) is \( Q \).

Answer:

\( QT \), \( QR \)

Part (b)