Final answer:
Line AB bisects ∠HAT into two equal angles. Since ∠HAB = 2x and ∠HAT = 8 degrees, by solving the equation 4x = 8, we determine that x equals 2 degrees.
Step-by-step explanation:
We are given that line AB bisects ∠HAT, which means AB divides ∠HAT into two equal angles. Since ∠HAB is given as 2x and it is half of ∠HAT, and the total measure of ∠HAT is given as 8 degrees, we can set up the equation 2x + 2x = 8 to find the value of x.
To solve for x, combine like terms to get 4x = 8. Then, divide both sides of the equation by 4 to get x = 2. This means the value of x is 2 degrees, which makes ∠HAB also 2x or 4 degrees. Dividing both sides of the equation by 2, we get x = 4. So, the value of x is 4. Therefore, the correct answer is (b) 4.