Question

ej bisects \\( \angle def \\), \\( m \angle dej = 5 x + 7 \\), \\( m \angle jef = 8 x - 8 \\). find x. 5 2 6 13

Explanation:

Step1: Use the angle - bisector property

Since \(\overrightarrow{EJ}\) bisects \(\angle DEF\), then \(m\angle DEJ=m\angle JEF\).
So, \(5x + 7=8x-8\).

Step2: Solve the equation for \(x\)

Subtract \(5x\) from both sides: \(7 = 8x-5x - 8\), which simplifies to \(7 = 3x-8\).
Add \(8\) to both sides: \(7 + 8=3x\), so \(15 = 3x\).
Divide both sides by \(3\): \(x=\frac{15}{3}=5\).

Answer:

\(x = 5\)