Question

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

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\). For \(\angle EDF\) and \(\angle EDC\), they share a common side \(DE\) and their non - common sides \(DF\) and \(DC\) form a straight line (\(FC\) is a straight line). So \(\angle EDF+\angle EDC = 180^{\circ}\), they are supplementary.

Step2: Recall the definition of vertical angles

Vertical angles are a pair of non - adjacent angles formed by the intersection of two lines. For \(\angle BDC\) and \(\angle FDE\), there is no two - line intersection that forms them as non - adjacent angles in the given diagram.

Step3: Analyze \(\angle GBE\) and \(\angle DBC\)

Let's assume the lines. If we consider the angles around point \(B\) and the relationships with other lines (by the properties of angles formed by intersecting lines and transversals in a plane figure), we can find that \(\angle GBE\) and \(\angle DBC\) can be supplementary.

Answer:

B. \(\angle BDC\) is vertical to \(\angle FDE\)