Answer:
x = 27
Step-by-step explanation:
The line segment at ∠A is an angle bisector, hence the following ratios are equal.
[tex]\frac{AB}{AC }[/tex] = [tex]\frac{10}{14}[/tex]
[tex]\frac{x+8}{2x-5}[/tex] = [tex]\frac{10}{14}[/tex] ( cross- multiply )
10(2x - 5) = 14(x + 8) ← distribute parenthesis on both sides
20x - 50 = 14x + 112 ( subtract 14x from both sides )
6x - 50 = 112 ( add 50 to both sides )
6x = 162 ( divide both sides by 6 )
x = 27
