Question

given: $overline{ab}$ passes through $overline{cd}$ at point $e$. select the true statements below. $square$ $angle aed$ and $angle ceb$ are complementary angles $square$ $angle deb$ and $angle aec$ are supplementary angles (linear pair) $square$ $angle aed$ and $angle ceb$ are vertical angles $square$ $angle deb$ and $angle ceb$ are vertical angles $square$ $angle aed$ and $angle cea$ are supplementary angles (linear pair)

Explanation:

Step1: Recall angle - pair definitions

Complementary angles add up to 90 degrees. Supplementary angles add up to 180 degrees. Vertical angles are opposite angles formed by two intersecting lines. A linear - pair of angles are adjacent angles that are supplementary.

Step2: Analyze each statement

1. $\angle AED$ and $\angle CEB$:

• Since $\overline{AB}$ and $\overline{CD}$ intersect at $E$, $\angle AED$ and $\angle CEB$ are opposite angles. They are vertical angles. They are not complementary (there is no information suggesting their sum is 90 degrees).

1. $\angle DEB$ and $\angle AEC$:

• $\angle DEB$ and $\angle AEC$ are vertical angles, not a linear - pair (supplementary adjacent angles).

1. $\angle AED$ and $\angle CEB$:

• As mentioned before, they are vertical angles.

1. $\angle DEB$ and $\angle CEB$:

• $\angle DEB$ and $\angle CEB$ are adjacent angles that form a straight - line $\overline{CD}$. They are a linear - pair (supplementary), not vertical angles.

1. $\angle AED$ and $\angle CEA$:

• $\angle AED$ and $\angle CEA$ are adjacent angles that form a straight - line $\overline{AB}$. They are supplementary (a linear - pair).

Answer:

• $\angle AED$ and $\angle CEB$ are vertical angles
• $\angle AED$ and $\angle CEA$ are supplementary angles (linear pair)