Question

what is ( mangle dfc )? ( 45^{circ} ) ( 80^{circ} ) ( 125^{circ} ) ( 135^{circ} )

Explanation:

Step1: Find the measure of ∠AFD

Since ∠AFE and ∠AFD are supplementary (they form a linear pair), and ∠AFE = 125°, then ∠AFD=180° - 125° = 55°.

Step2: Calculate the sum of angles around point F

The sum of angles around a point is 360°. But we can also use the fact that ∠AFB + ∠BFC+∠CFD + ∠DFA= 180° (since AFD is a straight - line - related angle sum, considering the angles on one side of the line AD). We know ∠AFB = 45°, ∠AFD = 55°, and we want to find ∠DFC. Let ∠DFC=x. Then 45°+x + 55°=180°.

Step3: Solve for ∠DFC

Simplify the equation 45°+x + 55°=180° to x+100°=180°. Subtract 100° from both sides: x = 180°-100°=80°.

Answer:

80°