what is m∠dfc? 45° 80° 125° 135°

Explanation:

Step1: Recall angle - sum property at a point

The sum of angles around a point is $360^{\circ}$.

Step2: Let $m\angle DFC = x$.

We know that $125^{\circ}+45^{\circ}+x = 360^{\circ}- 180^{\circ}$ (since the non - overlapping part of the angles around point $F$ that we are interested in makes up a straight - line supplement).

Step3: Simplify the equation

$125^{\circ}+45^{\circ}+x=180^{\circ}$. $170^{\circ}+x = 180^{\circ}$.

Step4: Solve for $x$

$x=180^{\circ}-170^{\circ}=10^{\circ}$ (This is wrong. Let's use the vertical - angle property). Since $\angle AFE$ and $\angle DFC$ are vertical angles, and vertical angles are equal. We know that $\angle AFE = 125^{\circ}$, so $m\angle DFC=125^{\circ}$.

Answer:

$125^{\circ}$