Question

look at this diagram:
if (overleftrightarrow{eg}) and (overleftrightarrow{hj}) are parallel lines and (mangle gfi = 54^{circ}), what is (mangle efi)?

Explanation:

Step1: Recall the property of a straight - line angle

The sum of angles on a straight line is \(180^{\circ}\). For the straight line \(EG\) and the transversal \(DK\) intersecting at point \(F\), \(\angle GFI\) and \(\angle EFI\) form a linear pair.

Step2: Set up the equation

Let \(m\angle EFI=x\). Since \(\angle GFI + \angle EFI=180^{\circ}\) (linear - pair property) and \(m\angle GFI = 54^{\circ}\), we have the equation \(x + 54^{\circ}=180^{\circ}\).

Step3: Solve the equation for \(x\)

Subtract \(54^{\circ}\) from both sides of the equation \(x+54^{\circ}=180^{\circ}\). So, \(x=180^{\circ}- 54^{\circ}\).

$$x = 126^{\circ}$$

Answer:

\(126\)