Question

in the diagram, which angle is part of a linear pair and part of a vertical pair?
∠bfc
∠cfg
∠gfd
∠efa

Explanation:

Step1: Recall linear - pair and vertical - pair definitions

A linear pair of angles is a pair of adjacent angles whose non - common sides are opposite rays and their sum is 180°. Vertical angles are non - adjacent angles formed by two intersecting lines.

Step2: Analyze each option

• For ∠BFC: It may be part of a linear pair but not easily identifiable as part of a vertical pair in the given diagram context.
• For ∠CFG: It can form a linear pair with ∠GFD (since they are adjacent and their non - common sides are opposite rays) and also forms a vertical pair with ∠EFA (non - adjacent angles formed by the intersection of lines).
• For ∠GFD: It is part of a linear pair with ∠CFG but has less obvious vertical - pair relationships compared to ∠CFG.
• For ∠EFA: It has a vertical - pair relationship with ∠CFG but may not be as clearly part of a linear pair as ∠CFG in the given layout.

Answer:

∠CFG