To find the value of \( x \) given the angles \( 23^\circ, 67^\circ, \) and \( 113^\circ \), we need to know the relationship or rule that applies to these angles. If the angles are part of a geometric figure (like a triangle, quadrilateral, etc.) or if they follow a specific rule (like all angles summing up to a certain value), we can find \( x \).
However, without additional context, I will assume we need to find an \( x \) that adds up to \( 360^\circ \), which is common in problems involving angles, or it can also mean they may sum up to a different value depending on the shape.
- If they are all angles in a quadrilateral, the sum of angles in a quadrilateral is \( 360^\circ \):
\[ 23^\circ + 67^\circ + 113^\circ + x^\circ = 360^\circ \]
Calculating the sum of known angles:
\[ 23 + 67 + 113 = 203 \]
Now, we can solve for \( x \):
\[ 203 + x = 360 \]
Subtracting 203 from both sides gives:
\[ x = 360 - 203 = 157^\circ \]
Thus, if \( x \) is calculated based on the sum of angles in a quadrilateral, then:
\[ x = 157^\circ \]
If you have a different context or a specific condition for the angles, please provide that for a more tailored answer!