Question

look at this diagram:
if (overleftrightarrow{eg}) and (overleftrightarrow{hj}) are parallel lines and (mangle gfi = 110^{circ}), what is (mangle efd)?
(70^{circ})
(110^{circ})
(180^{circ})
(120^{circ})

Explanation:

Step1: Use the linear - pair relationship

We know that \(\angle GFI\) and \(\angle EFD\) form a linear pair. The sum of angles in a linear pair is \(180^{\circ}\).
So, \(m\angle GFI + m\angle EFD=180^{\circ}\).

Step2: Solve for \(m\angle EFD\)

Given \(m\angle GFI = 110^{\circ}\). Substitute into the equation:
\(m\angle EFD=180^{\circ}-m\angle GFI\).
\(m\angle EFD = 180^{\circ}- 110^{\circ}\).
\(m\angle EFD=70^{\circ}\).

Answer:

\(70^{\circ}\) (the first option)