To find the value of \( x \) in the context of angles, we'll need to determine if these angles are part of a specific geometric configuration, such as a triangle or a straight line. Since the problem doesn’t specify this, we can explore both scenarios.
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If the angles are part of a triangle: The sum of the angles in a triangle is \( 180 \) degrees.
\[ 40^\circ + 83^\circ + x = 180^\circ \]
Now, add the known angles:
\[ 123^\circ + x = 180^\circ \]
To find \( x \), subtract \( 123^\circ \) from both sides:
\[ x = 180^\circ - 123^\circ = 57^\circ \]
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If the angles are in a straight line: The sum of the angles on a straight line is \( 180 \) degrees.
\[ 40^\circ + 83^\circ + x = 180^\circ \]
Again, add the known angles:
\[ 123^\circ + x = 180^\circ \]
To find \( x \), subtract \( 123^\circ \):
\[ x = 180^\circ - 123^\circ = 57^\circ \]
In both scenarios, we arrive at the same conclusion.
Thus, the value of \( x \) is:
\[ \boxed{57} \text{ degrees} \]