Question

bd and eg are parallel lines. which angles are supplementary angles? ∠gfh and ∠dcf ∠gfh and ∠efh ∠gfh and ∠bca ∠gfh and ∠efc

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze \(\angle GFH\) and \(\angle EFH\)

Since \(E\), \(F\), \(G\) are colinear (points on a straight - line), \(\angle GFH+\angle EFH = 180^{\circ}\) (by the linear - pair postulate: if two adjacent angles form a straight - line, their sum is \(180^{\circ}\)).

Step3: Analyze \(\angle GFH\) and \(\angle DCF\)

\(\angle GFH\) and \(\angle DCF\): There is no property (such as parallel - line properties like corresponding, alternate - interior, or same - side interior angles) or angle - addition postulate that would make \(\angle GFH+\angle DCF = 180^{\circ}\).

Step4: Analyze \(\angle GFH\) and \(\angle BCA\)

\(\angle GFH\) and \(\angle BCA\): There is no property (such as parallel - line properties like corresponding, alternate - interior, or same - side interior angles) or angle - addition postulate that would make \(\angle GFH+\angle BCA=180^{\circ}\).

Step5: Analyze \(\angle GFH\) and \(\angle EFC\)

\(\angle GFH\) and \(\angle EFC\): There is no property (such as parallel - line properties like corresponding, alternate - interior, or same - side interior angles) or angle - addition postulate that would make \(\angle GFH+\angle EFC = 180^{\circ}\).

Answer:

\(\angle GFH\) and \(\angle EFH\)