Question

1 multiple choice 4 points
in the figure below, \\( \overleftrightarrow { c d } \\) intersects \\( \overleftrightarrow { a b } \\) at \\( f, m \angle c f b = 50 ^ { \circ } \\), and \\( \angle e f a \cong \angle a f d \\).
what is \\( m \angle e f c \\)?
\\( 40 ^ { \circ } \\)
\\( 70 ^ { \circ } \\)
\\( 80 ^ { \circ } \\)
\\( 50 ^ { \circ } \\)

Explanation:

Step1: Find \(m\angle AFD\)

Since \(\angle CFB\) and \(\angle AFD\) are vertical angles, \(m\angle AFD=m\angle CFB = 50^{\circ}\).

Step2: Use the property of \(\angle EFA\cong\angle AFD\)

Given \(\angle EFA\cong\angle AFD\), so \(m\angle EFA = m\angle AFD=50^{\circ}\).

Step3: Calculate \(m\angle EFC\)

We know that \(\angle EFC+\angle EFA+\angle AFD = 180^{\circ}\) (straight - line angle). Let \(x = m\angle EFC\). Then \(x + 50^{\circ}+50^{\circ}=180^{\circ}\).

$$x=180^{\circ}-(50^{\circ}+50^{\circ})$$

$$x = 80^{\circ}$$

Answer:

\(80^{\circ}\)