Question

ce and fh are parallel lines. which angles are supplementary angles? ∠fgd and ∠edg ∠fgd and ∠fgi ∠fgd and ∠cdb ∠fgd and ∠hgi

Explanation:

Step1: Recall supplementary - angle definition

Two angles are supplementary if their sum is 180°. Adjacent angles that form a straight - line are supplementary.

Step2: Analyze each option

• For ∠FGD and ∠EDG: They are alternate interior angles (because CE∥FH), and they are not supplementary.
• For ∠FGD and ∠FGI: ∠FGD and ∠FGI form a linear pair. A linear pair of angles is adjacent and their non - common sides form a straight line. So, ∠FGD+∠FGI = 180°, and they are supplementary.
• For ∠FGD and ∠CDB: ∠CDB and ∠FGD are vertical - angle related to corresponding angles formed by the parallel lines CE and FH, and they are not supplementary.
• For ∠FGD and ∠HGI: ∠HGI and ∠FGD are vertical angles, and vertical angles are equal, not supplementary.

Answer:

∠FGD and ∠FGI