Question

look at this diagram:
if (overleftrightarrow{eg}) and (overleftrightarrow{hj}) are parallel lines and (mangle efi = 140^{circ}), what is (mangle efd)?

Explanation:

Step1: Find the relationship between angles

Since $\angle EFI$ and $\angle EFD$ are supplementary angles (they form a linear pair).

Step2: Use the supplementary - angle formula

The formula for supplementary angles is $m\angle EFI + m\angle EFD=180^{\circ}$.
Given $m\angle EFI = 140^{\circ}$, we substitute into the formula:
$140^{\circ}+m\angle EFD = 180^{\circ}$.

Step3: Solve for $m\angle EFD$

Subtract $140^{\circ}$ from both sides of the equation:
$m\angle EFD=180^{\circ}-140^{\circ}$.

Answer:

$40$