Question

ad = db and ae = ec. ef = 5 and m∠aed = 32°.
a
d
e
b
f
c
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

\( \angle AED \) and \( \angle ECF \) are alternate interior angles because \( DE \parallel BC \) and \( AC \) is a transversal. Alternate interior angles are equal.

Step3: Determine \( m\angle ECF \)

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

Answer:

\( 32 \)