Question

what is m∠dfc? 45° 80° 125° 135°

Explanation:

Step1: Recall angle - sum property of angles around a point

The sum of angles around a point is 360°.

Step2: Identify known angles

We know that one angle is 125° and another is 45°. Let \(m\angle DFC=x\). Since \(\angle AFE\) and the 125 - degree angle are vertical angles, \(m\angle AFE = 125^{\circ}\), and \(\angle BFC = 45^{\circ}\). Also, \(\angle AFE\) and \(\angle BFD\) are vertical angles, so \(m\angle BFD=125^{\circ}\), and \(\angle AFB\) and \(\angle DFC\) are vertical angles.

Step3: Calculate the unknown angle

We know that \(m\angle AFB + m\angle BFC+m\angle DFC+m\angle AFE=360^{\circ}\). Since \(\angle AFB\) and \(\angle DFC\) are vertical angles and \(\angle BFC = 45^{\circ}\), \(\angle AFE = 125^{\circ}\), and substituting into the equation we get \(x + 45^{\circ}+x+125^{\circ}=360^{\circ}\). Combining like - terms gives \(2x+170^{\circ}=360^{\circ}\). Subtracting 170° from both sides: \(2x=360^{\circ}-170^{\circ}=190^{\circ}\), then \(x = 80^{\circ}\).

Answer:

80°