https://file.aiquickdraw.com/mathbot/file/1729604862893xa5b0hln.jpg

The image shows two angles with values: \( 112^\circ \) and \( (3x + 11)^\circ \), along with red arrows indicating that these angles may be adjacent. Given the appearance, these angles likely form a linear pair, meaning they add up to \( 180^\circ \).

To solve for \( x \):

1. Since the angles form a linear pair, their sum is \( 180^\circ \). So,
   \[
   112^\circ + (3x + 11)^\circ = 180^\circ
   \]

2. Simplify the equation:
   \[
   112 + 3x + 11 = 180
   \]
   \[
   123 + 3x = 180
   \]

3. Subtract 123 from both sides:
   \[
   3x = 180 - 123
   \]
   \[
   3x = 57
   \]

4. Divide both sides by 3:
   \[
   x = \frac{57}{3}
   \]
   \[
   x = 19
   \]

Thus, the value of \( x \) is 19.

Would you like further clarification or details on this solution?

Here are 5 related questions:
1. How do you solve for \( x \) when angles form supplementary pairs?
2. Can adjacent angles be non-supplementary?
3. How do vertical angles relate to each other in a similar context?
4. What happens if the angles do not form a linear pair but instead a triangle?
5. Can angles greater than 180° exist in a real-world problem like this?

**Tip:** When working with angle pairs, remember that linear pairs always add up to 180°, while vertical angles are congruent.

Given two angles, one is 112° and the other is (3x + 11)°, forming a linear pair. Find the value of x.

This problem involves finding the unknown value of x by setting up an equation using the linear pair theorem. With one angle given as 112° and the other as (3x + 11)°, the solution shows step-by-step algebra to find x = 19. This exercise covers algebraic and geometric concepts suitable for Grades 8-10.

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