Let's solve each of these questions step by step:

Question 8

Given that TV bisects $\angle STU$, and
$m\angle STV = 27 + 3x \quad \text{and} \quad m\angle UTV = -5 + 7x.$
Since $TV$ bisects $\angle STU$, we know:
$m\angle STV = m\angle UTV.$
Set the two expressions equal to each other:
$27 + 3x = -5 + 7x.$
Solve for $x$:
$27 + 5 = 7x - 3x \quad \Rightarrow \quad 32 = 4x \quad \Rightarrow \quad x = 8.$

Now substitute $x = 8$ into $m\angle STV$:
$m\angle STV = 27 + 3(8) = 27 + 24 = 51^\circ.$

Since $TV$ bisects $\angle STU$, we know:
$m\angle STU = 2 \times m\angle STV = 2 \times 51 = 102^\circ.$

Answer for Question 8: $m\angle STU = 102^\circ.$

Question 9

Given that TV bisects $\angle STU$, and
$m\angle STV = 64 + 2x \quad \text{and} \quad m\angle UTV = 46 + 8x.$
Since $TV$ bisects $\angle STU$, we have:
$m\angle STV = m\angle UTV.$
Set the two expressions equal:
$64 + 2x = 46 + 8x.$
Solve for $x$:
$64 - 46 = 8x - 2x \quad \Rightarrow \quad 18 = 6x \quad \Rightarrow \quad x = 3.$

Now substitute $x = 3$ into $m\angle STV$:
$m\angle STV = 64 + 2(3) = 64 + 6 = 70^\circ.$

Since $TV$ bisects $\angle STU$, we know:
$m\angle STU = 2 \times m\angle STV = 2 \times 70 = 140^\circ.$

Answer for Question 9: $m\angle STU = 140^\circ.$

Question 10

To find $\angle IOH$ from the protractor diagram:

From the image, $I$ aligns with 30° on the left, and $H$ aligns with 100° on the right.
The angle $\angle IOH$ is the difference between the two measurements:
$m\angle IOH = 100^\circ - 30^\circ = 70^\circ.$

Answer for Question 10: $m\angle IOH = 70^\circ.$

Do you want further clarification on any question? Let me know!

Here are some follow-up questions to expand your understanding:

1. How do you determine when an angle is bisected?
2. What is the relationship between the measures of $\angle STV$ and $\angle UTV$?
3. How can you verify that a protractor reading is correct?
4. What happens when an angle is not bisected, and how would you solve for $x$ then?
5. Can you extend this idea to trisection of an angle?

Tip: When dealing with angles, always check if the given conditions (like bisected angles) divide the overall angle into equal parts.