Question

which angles are supplementary to each other?
∠egf and ∠cgd
∠ega and ∠cgd
∠dgf and ∠egf
∠cgd and ∠dgf

Explanation:

Step1: Recall the definition of supplementary angles

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

Step2: Analyze each option

• For \(\angle EGF\) and \(\angle CGD\): There is no indication that their sum is \(180^{\circ}\).
• For \(\angle EGA\) and \(\angle CGD\): There is no indication that their sum is \(180^{\circ}\).
• For \(\angle DGF\) and \(\angle EGF\): There is no indication that their sum is \(180^{\circ}\).
• For \(\angle CGD\) and \(\angle DGF\): Since they form a linear pair (they are adjacent and their non - common sides form a straight line), by the linear pair postulate, \(\angle CGD+\angle DGF = 180^{\circ}\).

Answer:

\(\angle CGD\) and \(\angle DGF\)