Question

1. dashed box
2. ( angle efg ) and ( angle gfh ) form a linear pair.
3. ( mangle efg + mangle gfh = 180^circ )
4. definition of supplementary angles dashed box
5. ( angle efg ) and ( angle ghf ) are supplementary.
6. given (diagram)
7. definition of linear pair
8. definition of supplementary angles
9. substitution property of equality
10. dashed box

Explanation:

Step1: Analyze Step 6

Step 6 uses Substitution Property of Equality, so we substitute \( m\angle EFG + m\angle GFH = 180^\circ \) (from Step 5) with the relevant angles for \( \angle EFG \) and \( \angle GHF \) (assuming \( m\angle GFH = m\angle GHF \) or relevant relation from diagram, but here we focus on the conclusion).

Step2: Apply Definition of Supplementary Angles

By the definition of supplementary angles, if the sum of two angles is \( 180^\circ \), they are supplementary. Since \( m\angle EFG + m\angle GHF = 180^\circ \) (from substitution), \( \angle EFG \) and \( \angle GHF \) are supplementary.

Answer:

\( \angle EFG \) and \( \angle GHF \) are supplementary (by Definition of Supplementary Angles, using Substitution Property of Equality from previous steps to show their measures sum to \( 180^\circ \)).