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This is a question involving angles formed by parallel lines and a transversal. The angles marked are \(136^\circ\) and \((3x + 1)^\circ\).

Since the two lines are parallel and a transversal cuts through them, the two angles shown are supplementary (they add up to 180°) because they form a linear pair.

We can set up the equation:

\[
136^\circ + (3x + 1)^\circ = 180^\circ
\]

Now, solve for \(x\):

1. Simplify the equation:
   \[
   136 + 3x + 1 = 180
   \]
   \[
   137 + 3x = 180
   \]

2. Subtract 137 from both sides:
   \[
   3x = 180 - 137
   \]
   \[
   3x = 43
   \]

3. Divide both sides by 3:
   \[
   x = \frac{43}{3} = 14.33
   \]

There seems to be no matching option for this exact decimal. Based on the provided answer choices, it seems the problem may expect a different interpretation or rounding. Would you like more details on the approach, or should we examine any potential issue further? Also, here are some expanded questions:

1. Why are the two angles supplementary in this scenario?
2. How are linear pairs of angles related?
3. What other angle relationships exist when parallel lines are cut by a transversal?
4. Could there be rounding or mistake in either the answer key or the equation setup?
5. How would you handle similar problems with angles on intersecting lines?

Tip: Always check if angles are supplementary, complementary, or equal when dealing with parallel lines and transversals.

What is the value of x in the diagram shown below?

Learn how to find the value of x in a diagram where angles formed by parallel lines and a transversal are supplementary. The problem involves algebraic expressions and the supplementary angle theorem. Ideal for students in Grades 7-9.

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