Question

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

Explanation:

Step1: Recall the definition of vertical angles

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

Step2: Analyze each angle

• For \(\angle EFA\): There is no angle formed by the intersection of the same two lines (as required for vertical angles) among the given options.
• For \(\angle BFC\): There is no angle formed by the intersection of the same two lines (as required for vertical angles) among the given options.
• For \(\angle GFD\): \(\angle EFA\) and \(\angle GFD\) are not formed by the intersection of the same two lines.
• For \(\angle CFG\): \(\angle EFA\) and \(\angle CFG\) are formed by the intersection of two lines. When two lines intersect, vertical angles are equal and non - adjacent. \(\angle EFA\) and \(\angle CFG\) meet these criteria.

Answer:

\(\angle CFG\)