Final answer:
To find the value of x, substitute the given values into the equation. Then, solve for x by simplifying the equation. To find the length of segment ef, substitute the value of x into the equation for ef and simplify.
Step-by-step explanation:
To find the value of x, we can use the information given in the question. Given that ef = 7x + 16, and eg = 204, we can substitute the value of ef with 7x + 16. Now, we have the equation 7x + 16 = 204. To find the length of segment ef, we can substitute the value of x into the equation for ef.
Simplifying the equation, we have 7x + 16 = 204. Subtracting 16 from both sides, we get 7x = 188. Dividing both sides by 7, we find that x = 26.
Now, substitute x = 26 back into the equation ef = 7x + 16. ef = (7 * 26) + 16 = 182 + 16 = 198. Therefore, the value of x is 26 and the length of segment ef is 198.