To find the value of \( x \) in the context provided, we need to clarify if the angles \( 27^\circ \), \( 63^\circ \), and \( 117^\circ \) are part of a specific geometric figure or scenario, such as a triangle, polygon, or linear angles, among others.
If we consider these angles as part of a triangle, the sum of the angles in a triangle is \( 180^\circ \). However, \( 27 + 63 + 117 = 207 \), which exceeds \( 180^\circ \).
If these angles are part of a linear combination, like being on a straight line, the angles would need to sum to \( 180^\circ \):
\[ 27 + 63 + 117 + x = 180 \]
Calculating the sum of \( 27^\circ\), \( 63^\circ\), and \( 117^\circ \):
\[ 27 + 63 = 90 \] \[ 90 + 117 = 207 \] So we have: \[ 207 + x = 180 \]
Now, to find \( x \):
\[ x = 180 - 207 \] \[ x = -27 \]
If these angles instead refer to a configuration different from a triangle or a straightforward linear equation, or if they are part of a cycle (where they must sum to \( 360^\circ \)), please provide more details. However, based on what we've calculated here, in this configuration, \( x = -27^\circ \).