Question

consider \\( \angle q \\).
which statement about the angle cannot be assumed from the diagram?
\\( \bigcirc \\) \\( \angle q \\) is a right angle.
\\( \bigcirc \\) the vertex of the angle is point \\( q \\).
\\( \bigcirc \\) the sides of \\( \angle q \\) are \\( \overrightarrow{qp} \\) and \\( \overrightarrow{qr} \\).
\\( \bigcirc \\) other names of the angle are \\( \angle pqr \\) and \\( \angle rqp \\).

Explanation:

• In geometry, an angle is named by its vertex. Here, the vertex is \(Q\), so the vertex of \(\angle Q\) is \(Q\).
• The sides of an angle are the two rays that form the angle. For \(\angle Q\), the rays are \(\overrightarrow{QP}\) and \(\overrightarrow{QR}\).
• An angle can also be named using three points: the vertex in the middle. So \(\angle Q\) can be named \(\angle PQR\) or \(\angle RQP\).
• However, there is no indication (like a right - angle symbol) in the diagram that \(\angle Q\) is a right angle.

Answer:

\(\angle Q\) is a right angle.