Question

which statement is true? o ∠cbe and ∠deb are alternate angles. o ∠feg and ∠deb are same - side interior angles. o ∠cbe and ∠deb are same - side interior angles. o ∠feg and ∠cbe are alternate angles.

Explanation:

Step1: Recall angle - pair definitions

Alternate angles are non - adjacent angles on opposite sides of a transversal. Same - side interior angles are on the same side of the transversal and between the two lines.

Step2: Analyze \(\angle CBE\) and \(\angle DEB\)

\(\angle CBE\) and \(\angle DEB\) are on the same side of the transversal \(AB\) and between the lines \(CH\) and \(DG\). So they are same - side interior angles.

Step3: Analyze \(\angle FEG\) and \(\angle DEB\)

\(\angle FEG\) and \(\angle DEB\) are vertical angles, not same - side interior angles.

Step4: Analyze \(\angle FEG\) and \(\angle CBE\)

\(\angle FEG\) and \(\angle CBE\) are not alternate angles.

Answer:

\(\angle CBE\) and \(\angle DEB\) are same - side interior angles.