Question

what is ( mangle edf )?
( mangle edf=square^{circ} )

Explanation:

Step1: Recall the sum of angles around a point

The sum of angles around a point \(D\) is \(360^{\circ}\).

Step2: Set up the equation

Let \(m\angle EDF = x\). Then \(65^{\circ}+65^{\circ}+143^{\circ}+x = 360^{\circ}\).

Step3: Simplify the left - hand side

\(65 + 65+143+x=(65 + 65)+143+x = 130+143+x=273 + x\).

Step4: Solve for \(x\)

Subtract \(273^{\circ}\) from both sides of the equation \(273+x = 360\). So \(x=360 - 273\).
\(x = 87^{\circ}\).

Answer:

\(87\)