Question

select all the pairs of adjacent angles.
∠ijg and ∠ijl ∠hge and ∠hgj
∠hgj and ∠fgj ∠kjg and ∠ijg

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 \(\angle IJG\) and \(\angle IJL\)

• Common vertex: \(J\)
• Common side: \(JI\)
• Non - common sides \(JG\) and \(JL\) are on opposite sides of \(JI\). So they are adjacent.

Step3: Analyze \(\angle HGE\) and \(\angle HGJ\)

• Common vertex: \(G\)
• Common side: \(GH\)
• Non - common sides \(GE\) and \(GJ\) are on opposite sides of \(GH\). So they are adjacent.

Step4: Analyze \(\angle HGJ\) and \(\angle FGJ\)

• Common vertex: \(G\)
• Common side: \(GJ\)
• Non - common sides \(GH\) and \(GF\) are on opposite sides of \(GJ\). So they are adjacent.

Step5: Analyze \(\angle KJG\) and \(\angle IJG\)

• Common vertex: \(J\)
• Common side: \(JG\)
• Non - common sides \(JK\) and \(JI\) are on opposite sides of \(JG\). So they are adjacent.

Answer:

The pairs of adjacent angles are \(\angle IJG\) and \(\angle IJL\), \(\angle HGE\) and \(\angle HGJ\), \(\angle HGJ\) and \(\angle FGJ\), \(\angle KJG\) and \(\angle IJG\) (all the given pairs are adjacent as per the definition of adjacent angles).