Question

which angles are supplementary angles?
∠cdb and ∠edg ∠cdb and ∠fgd
∠cdb and ∠hgi ∠cdb and ∠edb

Explanation:

Step1: Recall Supplementary Angles

Supplementary angles are two angles whose sum is \(180^\circ\) (a straight angle). They can be adjacent (forming a linear pair) or non - adjacent.

Step2: Analyze Each Option

• Option 1: \(\angle CDB\) and \(\angle EDG\) - These are vertical angles (if lines intersect), vertical angles are equal, not supplementary (unless each is \(90^\circ\), which is not indicated here).
• Option 2: \(\angle CDB\) and \(\angle FGD\) - There is no indication that these angles sum to \(180^\circ\). The lines \(FH\) and \(CE\) seem parallel, and \(\angle FGD\) and \(\angle CDB\) are corresponding or alternate angles (if parallel), so they are equal, not supplementary.
• Option 3: \(\angle CDB\) and \(\angle HGI\) - \(\angle HGI\) and \(\angle FGD\) are vertical angles, so \(\angle HGI=\angle FGD\). As in option 2, \(\angle CDB\) and \(\angle HGI\) are equal, not supplementary.
• Option 4: \(\angle CDB\) and \(\angle EDB\) - \(\angle CDB\) and \(\angle EDB\) form a linear pair (they are adjacent and their non - common sides form a straight line). So their sum is \(180^\circ\), meaning they are supplementary.

Answer:

\(\angle CDB\) and \(\angle EDB\)