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

∠EFA

Step-by-step explanation:

Linear pair : A linear pair is a pair of adjacent angles formed when two lines intersect and the sum of these angles is 180°

Vertical angles: The opposite angles formed by the two intersecting lines are called vertical angles.

Option 1) ∠BFC

Line BE and CF intersect at point F

So, the two adjacent angles formed when two lines intersect are ∠BFC and ∠EFC.

These are linear pair.

So,  ∠BFC is a part of linear pair.

Now by the definition of vertical angles , ∠BFC has no vertical pair.

So, ∠BFC is not a part of vertical pair.

Option 2) ∠CFG

According to the definition of linear pair ∠CFG is not a part of linear pair.

According to the definition of vertical pair ∠CFG is not a part of vertical pair.

Option 3) ∠GFD

According to the definition of linear pair ∠GFD has a linear pair ∠AFG

Thus ∠GFD is a part of linear pair

According to the definition of vertical pair ∠GFD is not a part of vertical pair.

Option 4) ∠EFA

According to the definition of linear pair ∠EFA has a linear pair ∠EFD

Thus ∠EFA is a part of linear pair

According to the definition of vertical pair ∠EFA has a ∠BFD vertical pair.

Thus ∠EFA is a part of vertical pair.

Hence ∠EFA is part of a linear pair and part of a vertical pair.