https://file.aiquickdraw.com/mathbot/file/1725568741932khumg1sc.jpg

In the image, we are given two angles adjacent to each other that form a right angle (90°). These angles are labeled as:

- \( (8x - 30)^\circ \)
- \( (4x)^\circ \)

Since the angles together form a right angle, their sum must equal 90°. Therefore, we can set up the following equation:

\[
(8x - 30) + 4x = 90
\]

### Solving the equation:
1. Combine like terms:
\[
8x - 30 + 4x = 90
\]
\[
12x - 30 = 90
\]

2. Add 30 to both sides:
\[
12x = 120
\]

3. Divide by 12:
\[
x = 10
\]

### Therefore, the value of \( x \) is 10.

Let me know if you'd like more details or have any questions! 

Here are 5 related questions you might consider:
1. What is the measure of each individual angle when \( x = 10 \)?
2. How would the equation change if the angles formed a straight line instead of a right angle?
3. Can you verify the solution by plugging \( x = 10 \) back into the angle expressions?
4. How can you check whether your final answer satisfies the original condition of forming a right angle?
5. How would the setup differ if the angles were given as complementary (adding up to 180°)?

**Tip**: Always remember that complementary angles add up to 90°, while supplementary angles add up to 180°.

This math problem involves finding the value of x for two adjacent angles that form a right angle. The angles are given by expressions (8x - 30)° and (4x)°. The sum of the angles is 90°, and solving for x requires basic algebraic manipulation.

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