Question

1. which of the following is a fully inscribed angle?

∠usr
∠pvu
∠tsr
∠qus

Explanation:

Step1: Recall the definition of an inscribed angle

An inscribed angle is an angle whose vertex is on the circle and whose sides contain chords of the circle.

Step2: Analyze each option

• $\angle USR$: The vertex \(S\) is on the circle, but one side \(SR\) is not a chord (it is a tangent - like ray).
• $\angle PVU$: The vertex \(V\) is the center of the circle, so it is a central angle, not an inscribed angle.
• $\angle TSR$: The vertex \(S\) is on the circle, but one side \(SR\) is not a chord (it is a tangent - like ray).
• $\angle QUS$: The vertex \(U\) is on the circle and both sides \(QU\) and \(SU\) are chords of the circle.

Answer:

\(\angle QUS\)