To find the measure of angle \( U \) in the given diagram with the angles provided:
- We know that in a straight line, the sum of angles is \( 180^\circ \).
- You have \( m∠A = 93^\circ \), \( mAU \text{ (which is the angle at point A)} = 126^\circ \), and \( mQU \text{ (which is the angle at point Q)} = 90^\circ \).
Since angles \( A \), \( U \), and \( Q \) might form a complete circle (or closed system), we can sum up the angles:
\[ m∠A + m∠QU + m∠U = 180^\circ \]
This equation holds true if \( A \), \( U \), and \( Q \) are on the same line.
Substituting the known angles into our equation:
\[ 93^\circ + 90^\circ + m∠U = 180^\circ \]
Now, simplifying this:
\[ 183^\circ + m∠U = 180^\circ \]
To isolate \( m∠U \), we subtract \( 183^\circ \) from both sides:
\[ m∠U = 180^\circ - 183^\circ \] \[ m∠U = -3^\circ \]
This shows that given the initial assumptions about angles \( A \), \( U \), and \( Q \) being in the same straight line is incorrect since angles cannot be negative.
In traditional configurations and euclidean geometry, a scenario where angles total greater than 180° defies the spatial rules unless there's overlap or misinterpretation of angle placement.
For a more accurate response, please confirm the locations of points A, U, and Q or clarify the relationships among the angles. If angles are part of different polygons or configurations, identifying the relationships and layout matters in accurately deriving the angle \( U \).