Question

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

Explanation:

1. Define key terms:

• A linear pair consists of two adjacent angles that form a straight line, so their sum is $180^\circ$.
• Vertical angles are opposite angles formed by intersecting lines, so they are congruent.

1. Analyze each option:

• $\angle BFC$: Forms a linear pair with $\angle CFA$, but has no vertical angle pair in the diagram.
• $\angle CFG$: Has no vertical angle pair, and does not form a linear pair with another angle.
• $\angle GFD$: Forms a linear pair with $\angle GFA$ (they make a straight line $AD$), and is a vertical angle with $\angle BFE$ (opposite angles from intersecting lines $BE$ and $AD$).
• $\angle EFA$: Forms a linear pair with $\angle EFD$, but has no vertical angle pair in the diagram.

Answer:

$\angle GFD$