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 - angle definition

Vertical angles are formed when two lines intersect. They are opposite each other and have equal measures.

Step2: Analyze each option

• $\angle ABE$ and $\angle ABC$ share a common side, so they are not vertical angles.
• $\angle ABE$ and $\angle CBD$ are vertical angles as they are opposite each other when the two lines intersect.
• $\angle ABE$ and $\angle EBD$ are adjacent angles, not vertical angles.
• $\angle ABC$ and $\angle EBD$ are vertical angles as they are opposite each other when the two lines intersect.
• $\angle ABC$ and $\angle CBD$ share a common side, so they are not vertical angles.

Answer:

$\angle ABE$ and $\angle CBD$, $\angle ABC$ and $\angle EBD$