Question

In the diagram, which angle is part of a linear pair and part of a vertical pair?

BFC
CFG
GFD
EFA

Answer 1

Answer:

∠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.

Answer 2

Answer:

D) EFA

Step-by-step explanation:

Let's see the definition of linear pair and vertical angles.

A linear pair of angles are the adjacent angles, when the angles add upto 180°.

Vertical angles are the  opposite angles when the two lines are intersecting. The vertical angles are equal in measure.

In the given figure there are only two lines, they are AD and BE. Othere are just rays.

By look at the figure, ∠EFA is a linear pair to∠EFD and as well as vertical angle to ∠DFB.

Therefore, the answer is D) EFA