https://file.aiquickdraw.com/mathbot/file/1725373427471u69by6tj.jpg

The image asks to find the values of \( x \) that lead to two decimal places, given that \( \angle EFG \) and \( \angle GFH \) are complementary angles.

To solve this problem, we need to understand that complementary angles sum up to 90 degrees.

From the image, it appears that:
- \( \angle EFG = 4x + 6^\circ \)
- \( \angle GFH = 2x - 11^\circ \)

Since the angles are complementary:
\[
(4x + 6) + (2x - 11) = 90
\]

Let's solve for \( x \).

Combining the like terms:
\[
4x + 2x + 6 - 11 = 90
\]
\[
6x - 5 = 90
\]

Add 5 to both sides:
\[
6x = 95
\]

Divide by 6:
\[
x = \frac{95}{6} \approx 15.83
\]

Therefore, the value of \( x \) to two decimal places is \( x = 15.83 \).

Would you like more details, or do you have any questions?

### Related Questions:
1. How do we determine if two angles are complementary?
2. How do you solve linear equations involving complementary angles?
3. What are the properties of complementary and supplementary angles?
4. What happens if the equation involves more than one unknown variable?
5. How do we handle problems involving degrees and radians?

**Tip:** Remember that complementary angles always add up to 90 degrees, and supplementary angles always add up to 180 degrees!

Find the values of x (rounded to two decimal places) given that ∠EFG and ∠GFH are complementary angles.

Learn how to find the value of x (rounded to two decimal places) for complementary angles ∠EFG = 4x + 6° and ∠GFH = 2x - 11°. This problem involves key algebraic concepts, suitable for students in Grades 8-10.

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