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To find the value of \( x \) in this quadrilateral, we can use the fact that the sum of the interior angles of any quadrilateral is \( 360^\circ \).

The angles in this quadrilateral are:
1. \( x + 20^\circ \)
2. \( 92^\circ \)
3. \( 86^\circ \)
4. \( x + 40^\circ \)

Let's set up the equation based on the angle sum:

\[
(x + 20) + 92 + 86 + (x + 40) = 360
\]

Combine like terms:

\[
2x + 238 = 360
\]

Now, subtract 238 from both sides:

\[
2x = 122
\]

Then, divide by 2:

\[
x = 61
\]

So, the value of \( x \) is \( 61^\circ \).

Would you like further details on this solution, or do you have any questions?

Here are some related questions for further exploration:
1. How do you find the sum of the interior angles of other polygons, such as pentagons or hexagons?
2. If the quadrilateral were a parallelogram, how would the angle relationships change?
3. How would you solve this if only three angles were given?
4. Can you prove why the interior angles of a quadrilateral always sum up to \( 360^\circ \)?
5. What is the approach for finding exterior angles in polygons?

**Tip:** When solving angle problems in polygons, always start by recalling the angle sum property specific to that shape.

Find the value of x given a quadrilateral with angles (x + 20)°, 92°, 86°, and (x + 40)°.

Learn how to find the value of x in a quadrilateral where the angles are given as (x + 20)°, 92°, 86°, and (x + 40)°. Using the angle sum property of quadrilaterals (sum of interior angles is 360°), we solve for x in this geometry problem. Suitable for students in Grades 7-9.

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