Question

ad = db and ae = ec. ef = 5 and m∠aed = 32°. m∠ecf = ?°

Explanation:

Step1: Identify Midsegments

Since \(AD = DB\) and \(AE = EC\), \(DE\) is the midsegment of \(\triangle ABC\). By the Midsegment Theorem, \(DE \parallel BC\).

Step2: Use Alternate Interior Angles

When two parallel lines (\(DE \parallel BC\)) are cut by a transversal (\(AC\)), alternate interior angles are equal. So \(\angle AED\) and \(\angle ECF\) are alternate interior angles.

Step3: Determine the Angle Measure

Given \(m\angle AED = 32^\circ\), we conclude \(m\angle ECF = m\angle AED = 32^\circ\).

Answer:

32