Question

which statement cannot be assumed based on the diagram?

∠cbd and ∠dbg are adjacent
∠bdc is vertical to ∠fde
∠gbe and ∠dbc are supplementary
∠edf and ∠edc are supplementary

Explanation:

Step1: Recall definitions

Adjacent angles share a common side and a common vertex. Vertical angles are opposite each other when two lines intersect. Supplementary angles add up to 180 degrees.

Step2: Analyze each option

• For $\angle CBD$ and $\angle DBG$, they share side $\overrightarrow{BD}$ and vertex $B$, so they are adjacent.
• $\angle BDC$ and $\angle FDE$ are not vertical angles as there is no clear indication that the lines forming them intersect in a way to create vertical - angle pairs.
• There is no information in the diagram to suggest that $\angle GBE$ and $\angle DBC$ are supplementary.
• $\angle EDF$ and $\angle EDC$ form a linear - pair (a straight - line $\overrightarrow{FC}$ with point $D$ on it), so they are supplementary.

Answer:

$\angle BDC$ is vertical to $\angle FDE$