Question

ce and fh are parallel lines. which angles are supplementary angles? ∠cdg and ∠hgd ∠fgi and ∠edb ∠cdg and ∠edb ∠edb and ∠cdb

Explanation:

Step1: Recall the definition of supplementary angles

Supplementary angles are two angles whose sum is \(180^{\circ}\).

Step2: Analyze \(\angle CDG\) and \(\angle HGD\)

Since \(\overleftrightarrow{CE}\parallel\overleftrightarrow{FH}\) and \(\overleftrightarrow{IB}\) is a transversal. \(\angle CDG\) and \(\angle HGD\) are same - side interior angles. By the same - side interior angles theorem, if two parallel lines are cut by a transversal, then the sum of same - side interior angles is \(180^{\circ}\).

Step3: Analyze \(\angle FGI\) and \(\angle EDB\)

\(\angle FGI\) and \(\angle EDB\) are not supplementary. \(\angle FGI\) and \(\angle CDG\) are vertical angles (\(\angle FGI=\angle CDG\) as vertical angles are equal). \(\angle CDG\) and \(\angle EDB\) are not supplementary.

Step4: Analyze \(\angle CDG\) and \(\angle EDB\)

\(\angle CDG\) and \(\angle EDB\) are vertical angles (\(\angle CDG = \angle EDB\)), and their sum is \(2\angle CDG
eq180^{\circ}\) (unless \(\angle CDG = 90^{\circ}\), but there is no indication of that from the parallel - line property).

Step5: Analyze \(\angle EDB\) and \(\angle CDB\)

\(\angle EDB\) and \(\angle CDB\) are adjacent angles. But there is no property (from the given parallel lines \(\overleftrightarrow{CE}\parallel\overleftrightarrow{FH}\)) that would make their sum \(180^{\circ}\).

Answer:

\(\angle CDG\) and \(\angle HGD\)