Answer:
[tex] x = 5 [/tex]
Step-by-step explanation:
Given that segment EJ bisects angle DEF, it implies that angle DEF is divided into two equal angles, namely, angle DEJ = 5x + 7, and angle JEF = 8x - 8.
To find the value of x, let's derive an equation by setting m<DEJ equal to m<JEF, since both are equal parts of angle DEF bisected by segment EJ.
Thus:
[tex] 5x + 7 = 8x - 8 [/tex]
Solve for x
[tex] 5x + 7 - 8x = 8x - 8 - 8x [/tex] (subtracting 8x from both sides)
[tex] -3x + 7 = - 8 [/tex]
[tex] -3x + 7 - 7 = - 8 - 7 [/tex] (Subtracting 7 from both sides)
[tex] -3x = -15 [/tex]
[tex] \frac{-3x}{-3} = \frac{-15}{-3} [/tex] (dividing both sides by -3)
[tex] x = 5 [/tex]
