Answer:
[tex]x=27[/tex]
Step-by-step explanation:
Notice that Angle A is being bisected.
Hence, we can use the Angle Bisector Theorem to write the following proportion:
[tex]\frac{x+8}{10}=\frac{2x-5}{14}[/tex]
Solve for x. Cross-multiply:
[tex]10(2x-5)=14(x+8)[/tex]
Distribute:
[tex]20x-50=14x+112[/tex]
Subtract 14x from both sides:
[tex]6x-50=112[/tex]
Add 50 to both sides:
[tex]6x=162[/tex]
Divide both sides by 6. Hence, the value of x is:
[tex]x=27[/tex]
