Question

which statement cannot be assumed based on the diagram? a) ∠gbe and ∠dbc are adjacent. b) ∠bdc is vertical to ∠fde. c) ∠edf and ∠edc are supplementary. d) ∠abg and ∠gbd are supplementary.

Explanation:

Step1: Recall adjacent - angle definition

Adjacent angles share a common side and a common vertex. $\angle GBE$ and $\angle DBC$ do not share a common side or a common vertex, so they are not adjacent.

Step2: Recall vertical - angle definition

Vertical angles are opposite each other when two lines intersect. $\angle BDC$ and $\angle FDE$ are vertical angles as lines $FC$ and $GE$ intersect at $D$.

Step3: Recall supplementary - angle definition

Supplementary angles add up to 180 degrees. $\angle EDF$ and $\angle EDC$ form a straight - line ($\angle FDC$), so they are supplementary. Also, $\angle ABG$ and $\angle GBD$ form a straight - line ($\angle ABD$), so they are supplementary.

Answer:

A. $\angle GBE$ and $\angle DBC$ are adjacent.