Question

select all the pairs of adjacent angles. ∠tsv and ∠rsv ∠uvx and ∠uvs ∠wvx and ∠uvx ∠wvs and ∠uvs

Explanation:

Step1: Recall adjacent angles definition

Adjacent angles share a common side and vertex, and their non - common sides are on opposite sides of the common side.

Step2: Analyze \(\angle TSV\) and \(\angle RSV\)

• Common vertex: \(S\)
• Common side: \(SV\) (or \(SR\) as they are colinear). The non - common sides \(ST\) and \(SR\) are on opposite sides of \(SV\). So they are adjacent.

Step3: Analyze \(\angle UVX\) and \(\angle UVS\)

• Common vertex: \(V\)
• Common side: \(UV\)
• Non - common sides \(VX\) and \(VS\) are on opposite sides of \(UV\). So they are adjacent.

Step4: Analyze \(\angle WVX\) and \(\angle UVX\)

• Common vertex: \(V\)
• Common side: \(VX\)
• Non - common sides \(WV\) and \(UV\) are on opposite sides of \(VX\). So they are adjacent.

Step5: Analyze \(\angle WVS\) and \(\angle UVS\)

• Common vertex: \(V\)
• Common side: \(VS\)
• Non - common sides \(WV\) and \(UV\) are on opposite sides of \(VS\). So they are adjacent.

Answer:

The pairs of adjacent angles are \(\boldsymbol{\angle TSV}\) and \(\boldsymbol{\angle RSV}\), \(\boldsymbol{\angle UVX}\) and \(\boldsymbol{\angle UVS}\), \(\boldsymbol{\angle WVX}\) and \(\boldsymbol{\angle UVX}\), \(\boldsymbol{\angle WVS}\) and \(\boldsymbol{\angle UVS}\) (all the checked pairs in the given options are correct as per the definition of adjacent angles).