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 definition

A linear pair is a pair of adjacent angles whose non - common sides are opposite rays.

Step2: Recall vertical angles definition

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines.

Step3: Analyze \( \angle GFD \)

• Linear pair: \( \angle GFD \) and \( \angle GFC \) form a linear pair (adjacent, non - common sides are opposite rays).
• Vertical pair: \( \angle GFD \) and \( \angle BFC \) are vertical angles (formed by the intersection of two lines).

Step4: Analyze other options

• For \( \angle BFC \): It has a vertical pair (\( \angle GFD \)) but no linear pair in the given options context.
• For \( \angle CFG \): It has a linear pair (\( \angle GFD \)) but no vertical pair as per the options.
• For \( \angle EFA \): It has neither a proper linear pair (as per the options) nor a vertical pair in the given diagram context.

Answer:

C. \( \angle GFD \)