Question

look at this diagram; if \\(\overleftrightarrow{df}\\) and \\(\overleftrightarrow{gi}\\) are parallel lines and \\(m\angle feh = 56^\circ\\), what is \\(m\angle fec\\)?

Explanation:

Step1: Identify angle relationship

Since \( \overleftrightarrow{DF} \) and \( \overleftrightarrow{GI} \) are parallel, and \( \angle FEH \) and \( \angle FEC \) are supplementary (they form a linear pair, so their measures add up to \( 180^\circ \)).

Step2: Calculate \( m\angle FEC \)

We know \( m\angle FEH = 56^\circ \), so \( m\angle FEC = 180^\circ - m\angle FEH \).
Substitute \( m\angle FEH = 56^\circ \) into the formula: \( m\angle FEC = 180^\circ - 56^\circ = 124^\circ \).

Answer:

\( 124 \)