Question

if \\( \overline { c d } \cong \overline { c f } \\) and \\( m \angle c e d = 53 ^ { \circ } \\), what is \\( m \angle d e f \\)?
\\( m \angle d e f = \square ^ { \circ } \\)

Explanation:

Step1: Use the property of angle bisector

Since \(CD\cong CF\), \(CE = CE\) (common side), and \(\angle CDE=\angle CFE = 90^{\circ}\) (right angles), by the Hypotenuse - Leg (HL) congruence criterion, \(\triangle CDE\cong\triangle CFE\). Then \(CE\) is the angle bisector of \(\angle DEF\).

Step2: Calculate \(\angle DEF\)

We know that if \(CE\) is the angle bisector of \(\angle DEF\), then \(\angle DEF = 2\angle CED\). Given \(m\angle CED=53^{\circ}\), so \(m\angle DEF = 2\times53^{\circ}\)

Answer:

\(106\)