Question

in the diagram, which angles are vertical angles? select two options. $\angle abe$ and $\angle abc$ $\angle abe$ and $\angle cbd$ $\angle abe$ and $\angle ebd$ $\angle abc$ and $\angle ebd$ $\angle abc$ and $\angle cbd$

Explanation:

Vertical angles are formed when two lines intersect, and they are opposite each other, sharing a common vertex but not a common side.

• For $\angle ABE$ and $\angle CBD$: Lines $AD$ and $EC$ intersect at $B$, so these angles are opposite (vertical angles).
• For $\angle ABC$ and $\angle EBD$: Similarly, they are opposite when lines $AD$ and $EC$ intersect at $B$, so they are vertical angles.
• $\angle ABE$ and $\angle ABC$: These are adjacent angles (share a common side $AB$ and vertex $B$), not vertical.
• $\angle ABE$ and $\angle EBD$: These are adjacent (share side $BE$) and form a linear pair, not vertical.
• $\angle ABC$ and $\angle CBD$: Adjacent, form a linear pair, not vertical.

Answer:

B. $\angle ABE$ and $\angle CBD$
D. $\angle ABC$ and $\angle EBD$