Question

1. if ( overleftrightarrow{de} parallel overleftrightarrow{gf} ), what is ( mangle dfg )?

( mangle dfg=)____( ^{circ} )

Explanation:

Step1: Find the adjacent angle to \(125^{\circ}\)

When two angles form a linear - pair, their sum is \(180^{\circ}\). Let the adjacent angle to \(125^{\circ}\) at point \(D\) be \(x\). Then \(x + 125^{\circ}=180^{\circ}\), so \(x = 180^{\circ}-125^{\circ}=55^{\circ}\).

Step2: Use the property of parallel lines

Since \(\overleftrightarrow{DE}\parallel\overleftrightarrow{GF}\), and the transversal intersects them. By the alternate - interior angles theorem, \(m\angle DFG\) is equal to the adjacent angle of \(125^{\circ}\) (because alternate - interior angles are congruent when two parallel lines are cut by a transversal).

Answer:

\(55\)