Question

in the diagram, which angles are vertical angles?
select two options.
□ ∠abe and ∠abc
□ ∠abe and ∠cbd
□ ∠abe and ∠ebd
□ ∠abc and ∠ebd
□ ∠abc and ∠cbd

Explanation:

Step1: Recall vertical angles definition

Vertical angles are formed when two lines intersect. They are opposite angles.

Step2: Analyze each option

• For $\angle ABE$ and $\angle ABC$: They are adjacent angles (share a common side $BE$ and $BC$ respectively with a common vertex $B$), not vertical angles.
• For $\angle ABE$ and $\angle CBD$: When lines $AE$ and $CD$ intersect at $B$, $\angle ABE$ and $\angle CBD$ are opposite angles.
• For $\angle ABE$ and $\angle EBD$: They are adjacent angles (form a linear - pair as they are on a straight line $AD$), not vertical angles.
• For $\angle ABC$ and $\angle EBD$: $\angle ABC$ and $\angle EBD$ are not formed by the intersection of two lines in the required vertical - angle - forming way.
• For $\angle ABC$ and $\angle CBD$: They are adjacent angles (share a common side $BC$), not vertical angles.

Answer:

$\angle ABE$ and $\angle CBD$