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We are given a diagram where:

- \(\angle KNL = 87^\circ\),
- \(\angle JNK = 42^\circ\), and
- \(\angle MNK = (8x + 7)^\circ\).

Since angles \(JNK\), \(KNL\), and \(MNL\) form a straight line around point \(N\), we know the sum of these angles must be \(180^\circ\).

Thus, we can set up the equation:

\[
\angle JNK + \angle KNL + \angle MNK = 180^\circ
\]

Substituting the given values:

\[
42^\circ + 87^\circ + (8x + 7)^\circ = 180^\circ
\]

Simplifying:

\[
129^\circ + (8x + 7)^\circ = 180^\circ
\]

\[
8x + 136^\circ = 180^\circ
\]

Now, subtract 136 from both sides:

\[
8x = 44^\circ
\]

Finally, divide by 8:

\[
x = 5.5
\]

Thus, the value of \(x\) is \(5.5\).

---

Do you need further clarification or details? 

Here are 5 questions to expand on this topic:
1. How do we define complementary and supplementary angles?
2. What are adjacent angles and how do they interact with straight angles?
3. How would the equation change if one of the angles were unknown?
4. How can we verify the correctness of the calculated \(x\)?
5. Can you find \(x\) if \(\angle KNL\) were \(90^\circ\) instead of \(87^\circ\)?

**Tip:** Always double-check that the sum of angles on a straight line equals 180° to avoid simple errors!

Find the value of x in the given geometric diagram where angles JNK, KNL, and MNK form a straight line.

Learn how to solve for x in a geometric diagram where angles JNK, KNL, and MNK form a straight line. This problem covers key geometric and algebraic concepts, suitable for students in Grades 7-9.

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