https://file.aiquickdraw.com/mathbot/file/17271934913288lwbxvl4.jpg

The image shows a quadrilateral \( JKLM \), where the interior angles are labeled as follows:

- \(\angle JKL = 105^\circ\)
- \(\angle KLM = 60^\circ\)
- \(\angle LMJ = 80^\circ\)
- \(\angle J = 39x - 2\)

Since the sum of the interior angles in any quadrilateral is \(360^\circ\), we can set up the equation to solve for \(x\):

\[
105^\circ + 60^\circ + 80^\circ + (39x - 2) = 360^\circ
\]

Let's simplify and solve for \(x\):

\[
245^\circ + 39x - 2 = 360^\circ
\]
\[
243^\circ + 39x = 360^\circ
\]
\[
39x = 360^\circ - 243^\circ
\]
\[
39x = 117^\circ
\]
\[
x = \frac{117^\circ}{39} = 3
\]

Thus, \( x = 3 \).

Would you like me to go into further details, or do you have any questions?

Here are 5 related questions for practice:
1. How would you calculate the sum of the interior angles for a polygon with more sides (e.g., a pentagon)?
2. What are the properties of a cyclic quadrilateral, and how do they affect the angles?
3. Can you use the same method to find unknown variables in a triangle’s angles?
4. What is the exterior angle theorem, and how can it be applied to polygons?
5. How can the Law of Cosines or Law of Sines be used in relation to quadrilaterals?

**Tip:** Always remember that the sum of interior angles of any polygon is \((n-2) \times 180^\circ\), where \(n\) is the number of sides.

The sum of the interior angles of quadrilateral JKLM is given. One angle is represented by the expression 39x - 2. The other angles are 105°, 60°, and 80°. Find the value of x.

In this geometry problem, solve for the variable x using the sum of the interior angles of a quadrilateral. The angles are provided as 105°, 60°, 80°, and 39x - 2°. This solution is ideal for students in Grades 8-10, covering algebraic and geometric concepts.

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