Question

if \\( \overline { d g } \cong \overline { f g } \\), \\( m \angle d e g = 4 a - 72 ^ { \circ } \\), and \\( m \angle f e g = 5 a - 91 ^ { \circ } \\), what is \\( m \angle d e g \\)?

Explanation:

Step1: Set up the equation

Since \( \overline{DG}\cong\overline{FG}\), by the Angle - Bisector Theorem, \(m\angle DEG = m\angle FEG\). So, \(4a - 72=5a - 91\).

Step2: Solve for \(a\)

Subtract \(4a\) from both sides: \(-72=a - 91\).
Add \(91\) to both sides: \(a=-72 + 91=19\).

Step3: Find \(m\angle DEG\)

Substitute \(a = 19\) into \(m\angle DEG=4a - 72\).
\(m\angle DEG=4\times19-72\).
\(m\angle DEG = 76-72\).

Answer:

\(4\)