Q36 - Geometry

Question

Given the diagram, state whether you can reach the conclusion shown.

$\angle AOE$ and $\angle AOD$ are adjacent angles.

Step-by-Step Solution

Answer

We cannot conclude that $\angle AOE$ and $\angle AOD$ are adjacent angles.

Step 1. Observe the given diagram.

Step 2. Highlight ∠AOE and ∠AOD in the given diagram.

Step 3. Explain whether you can reach the given conclusion.

Two angles in a plane that have a common vertex and a common side but no common interior points are called adjacent angles. $\angle AOE$ is a subset of $\angle AOD$ and point E is in the interior region of $\angle AOE$ and $\angle AOD$. Therefore, $\angle AOE$ and $\angle AOD$ are not adjacent angles even though they have a common vertex point O and common ray $\overline{OA}$.